Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measur...Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.展开更多
We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution co...We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.展开更多
We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed proces...We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.展开更多
We establish the Hausdorff dimension of the graph of general Markov processes on Rd based on some probability estimates of the processes staying or leaving small balls in small time.In particular,our results indicate ...We establish the Hausdorff dimension of the graph of general Markov processes on Rd based on some probability estimates of the processes staying or leaving small balls in small time.In particular,our results indicate that,for symmetric diffusion processes(withα=2)or symmetricα-stable-like processes(withα∈(0,2))on Rd,it holds almost surely that dimH GrX([0,1])=1{α<1}+(2−1/α)1{α≥1,d=1}+(d∧α)1{α≥1,d≥2}.We also systematically prove the corresponding results about the Hausdorff dimension of the range of the processes.展开更多
Motivated by some recent works on the topic of the Brown-Resnick process, we study the functional limit theorem for normalized pointwise maxima of dependent chi-processes. It is proven that the properly normalized poi...Motivated by some recent works on the topic of the Brown-Resnick process, we study the functional limit theorem for normalized pointwise maxima of dependent chi-processes. It is proven that the properly normalized pointwise maxima of those processes are attracted by the Brown-Resnick process.展开更多
With the projected global surge in hydrogen demand, driven by increasing applications and the imperative for low-emission hydrogen, the integration of machine learning(ML) across the hydrogen energy value chain is a c...With the projected global surge in hydrogen demand, driven by increasing applications and the imperative for low-emission hydrogen, the integration of machine learning(ML) across the hydrogen energy value chain is a compelling avenue. This review uniquely focuses on harnessing the synergy between ML and computational modeling(CM) or optimization tools, as well as integrating multiple ML techniques with CM, for the synthesis of diverse hydrogen evolution reaction(HER) catalysts and various hydrogen production processes(HPPs). Furthermore, this review addresses a notable gap in the literature by offering insights, analyzing challenges, and identifying research prospects and opportunities for sustainable hydrogen production. While the literature reflects a promising landscape for ML applications in hydrogen energy domains, transitioning AI-based algorithms from controlled environments to real-world applications poses significant challenges. Hence, this comprehensive review delves into the technical,practical, and ethical considerations associated with the application of ML in HER catalyst development and HPP optimization. Overall, this review provides guidance for unlocking the transformative potential of ML in enhancing prediction efficiency and sustainability in the hydrogen production sector.展开更多
Electron emission plays a dominant role in plasma-cathode interactions and is a key factor in many plasma phenomena and industrial applications.It is necessary to illustrate the various electron emission mechanisms an...Electron emission plays a dominant role in plasma-cathode interactions and is a key factor in many plasma phenomena and industrial applications.It is necessary to illustrate the various electron emission mechanisms and the corresponding applicable description models to evaluate their impacts on discharge properties.In this study,detailed expressions of the simplified formulas valid for field emission to thermo-field emission to thermionic emission typically used in the numerical simulation are proposed,and the corresponding application ranges are determined in the framework of the Murphy-Good theory,which is commonly regarded as the general model and to be accurate in the full range of conditions of the validity of the theory.Dimensionless parameterization was used to evaluate the emission current density of the Murphy-Good formula,and a deviation factor was defined to obtain the application ranges for different work functions(2.5‒5 eV),cathode temperatures(300‒6000 K),and emitted electric fields(10^(5) to 10^(10) V·m^(-1)).The deviation factor was shown to be a nonmonotonic function of the three parameters.A comparative study of particle number densities in atmospheric gas discharge with a tungsten cathode was performed based on the one-dimensional implicit particle-in-cell(PIC)with the Monte Carlo collision(MCC)method according to the aforementioned application ranges.It was found that small differences in emission current density can lead to variations in the distributions of particle number density due to changes in the collisional environment.This study provides a theoretical basis for selecting emission models for subsequent numerical simulations.展开更多
This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on r...This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path.Our approach is particularly suitable for high-frequency data.To formulate the parameter estimators,we introduce a theory of pathwise Itôintegrals with respect to fractional Brownian motion.By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes,we demonstrate that our estimators are strongly consistent and pathwise stable.Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings,and may have practical implications for fields including finance,economics,and engineering.展开更多
Recently published in Joule,Feng Liu and colleagues from Shanghai Jiaotong University reported a record-breaking 20.8%power conversion efficiency in organic solar cells(OSCs)with an interpenetrating fibril network act...Recently published in Joule,Feng Liu and colleagues from Shanghai Jiaotong University reported a record-breaking 20.8%power conversion efficiency in organic solar cells(OSCs)with an interpenetrating fibril network active layer morphology,featuring a bulk p-in structure and proper vertical segregation achieved through additive-assisted layer-by-layer deposition.This optimized hierarchical gradient fibrillar morphology and optical management synergistically facilitates exciton diffusion,reduces recombination losses,and enhances light capture capability.This approach not only offers a solution to achieving high-efficiency devices but also demonstrates the potential for commercial applications of OSCs.展开更多
Polygonati rhizoma is often used in Chinese medicine and as food.In this study,atmospheric pressure matrixassisted laser desorption ionization and quadruple-time-of-flight(MALDI-Q-TOF)mass spectrometry techniques were...Polygonati rhizoma is often used in Chinese medicine and as food.In this study,atmospheric pressure matrixassisted laser desorption ionization and quadruple-time-of-flight(MALDI-Q-TOF)mass spectrometry techniques were applied to P.rhizoma samples from Polygonatum cyrtonema Hua species.Positive ions were mainly detected in the mass range of m/z 200-600,while negative ions were mainly observed in the mass range of m/z 100-450.A total of 263 components were identified and the spatial distribution and changes in saccharides contents during the steaming process of P.rhizoma were investigated.Monosaccharide and disaccharide exhibit a relatively uniform distribution,while the oligosaccharides were mainly found in the bast of fresh P.rhizoma.Although the contents of monosaccharide and disaccharide were increased during steaming,that of trisaccharide,tetrasaccharide,and pentasaccharide were decreased.We used the 5 saccharide types with the greatest variation in content as variables for the principal component analysis(PCA)and cluster analysis.Both PCA and cluster analysis showed that these 5 saccharides can be used as markers in the steaming process of the P.rhizoma.Present study of mass spectrometry imaging provides novel insights into the spatiotemporal accumulation patterns of saccharides in P.rhizoma,improving our understanding of the steaming process.展开更多
This study focused on the production of polypropylene(PP)/silver(Ag)composites via additive manufacturing.This study aimed to enhance the quality of medical-grade PP in material extrusion(MEX)three-dimensional printin...This study focused on the production of polypropylene(PP)/silver(Ag)composites via additive manufacturing.This study aimed to enhance the quality of medical-grade PP in material extrusion(MEX)three-dimensional printing(3DP)by improving its mechanical properties while simultaneously adding antibacterial properties.The latter can find extremely important and versatile properties that are applicable in defense and security domains.PP/Ag nanocomposites were prepared using a novel method based on a reaction occurring while mixing appropriate quantities of the starting polymers and additives,namely polyvinylpyrrolidone(PVP)as the matrix material and silver nitrate(AgNO_(3))as the filler.This process produced three-dimensional(3D)printed filaments,which were then used to create specimens for a series of standardized tests.It was found that the mechanical properties of the nanocomposites were enhanced in relation to pristine PP,especially for the PP matrix with various loadings of AgNO_(3)and PVP,such as 5.0 wt%and 2.5 wt%,respectively.The voids,inclusions,and actual-to-nominal dimensions also showed improved results.The 3DP specimens exhibited a more effective biocidal performance against Staphylococcus aureus than Escherichia coli,which developed an inhibition zone only in the case of PP with filler loading percentages of AgNO_(3)and PVP at 10.0 wt%and 5.0 wt%,respectively Compounds possessing such properties can be beneficial for various applications requiring increased mechanical properties and biocidal capabilities,such as in the Defence or medical industries.展开更多
A new structure with the special property that catastrophes is imposed to ordinary Birth_Death processes is considered. The necessary and sufficient conditions of stochastically monotone, Feller and symmetric properti...A new structure with the special property that catastrophes is imposed to ordinary Birth_Death processes is considered. The necessary and sufficient conditions of stochastically monotone, Feller and symmetric properties for the extended birth_death processes with catastrophes are obtained.展开更多
This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is ...This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.展开更多
In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform Holder condition, and obtain the uniform packing dimension of mu...In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform Holder condition, and obtain the uniform packing dimension of multiparameter stable processes. If Z is a stable （N, d, α）-process and αN ≤ d, then the following holds with probability 1 Dim Z（E）=α Dim E for any Borel setE ∈B（R ＋^N）, where Z（E）={x：E←t∈E,Z（t）=x}, Dim （E） denotes the packing dimension of E.展开更多
One of the assumptions of previous research in evolutionary game dynamics is that individuals use only one rule to update their strategy. In reality, an individual's strategy update rules may change with the envir...One of the assumptions of previous research in evolutionary game dynamics is that individuals use only one rule to update their strategy. In reality, an individual's strategy update rules may change with the environment, and it is possible for an individual to use two or more rules to update their strategy. We consider the case where an individual updates strategies based on the Moran and imitation processes, and establish mixed stochastic evolutionary game dynamics by combining both processes. Our aim is to study how individuals change strategies based on two update rules and how this affects evolutionary game dynamics. We obtain an analytic expression and properties of the fixation probability and fixation times(the unconditional fixation time or conditional average fixation time) associated with our proposed process. We find unexpected results. The fixation probability within the proposed model is independent of the probabilities that the individual adopts the imitation rule update strategy. This implies that the fixation probability within the proposed model is equal to that from the Moran and imitation processes. The one-third rule holds in the proposed mixed model. However, under weak selection, the fixation times are different from those of the Moran and imitation processes because it is connected with the probability that individuals adopt an imitation update rule. Numerical examples are presented to illustrate the relationships between fixation times and the probability that an individual adopts the imitation update rule, as well as between fixation times and selection intensity. From the simulated analysis, we find that the fixation time for a mixed process is greater than that of the Moran process, but is less than that of the imitation process. Moreover, the fixation times for a cooperator in the proposed process increase as the probability of adopting an imitation update increases; however, the relationship becomes more complex than a linear relationship.展开更多
基金Supported by NNSF of China (10001020 and 10471003), Foundation for Authors Awarded Excellent Ph.D.Dissertation
文摘Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.
基金Supported by the Science and Technology Research Projects of Hubei Provincial Department of Education(B2022077)。
文摘We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.
基金partially supported by the National Natural Science Foundation of China(11871244)the Fundamental Research Funds for the Central Universities,JLU。
文摘We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.
基金supported by Leshan Normal University Scientific Research Start-up Project for Introducing High-level Talents(Grand No.RC2024001).
文摘We establish the Hausdorff dimension of the graph of general Markov processes on Rd based on some probability estimates of the processes staying or leaving small balls in small time.In particular,our results indicate that,for symmetric diffusion processes(withα=2)or symmetricα-stable-like processes(withα∈(0,2))on Rd,it holds almost surely that dimH GrX([0,1])=1{α<1}+(2−1/α)1{α≥1,d=1}+(d∧α)1{α≥1,d≥2}.We also systematically prove the corresponding results about the Hausdorff dimension of the range of the processes.
基金supported by the Zhejiang Provincial Natural Science Foundation of China(LY18A010020)the Innovation of Jiaxing City:A Program to Support the Talented Persons.
文摘Motivated by some recent works on the topic of the Brown-Resnick process, we study the functional limit theorem for normalized pointwise maxima of dependent chi-processes. It is proven that the properly normalized pointwise maxima of those processes are attracted by the Brown-Resnick process.
基金express their gratitude to the Higher Institution Centre of Excellence (HICoE) fund under the project code (JPT.S(BPKI)2000/016/018/015JId.4(21)/2022002HICOE)Universiti Tenaga Nasional (UNITEN) for funding the research through the (J510050002–IC–6 BOLDREFRESH2025)Akaun Amanah Industri Bekalan Elektrik (AAIBE) Chair of Renewable Energy grant,and NEC Energy Transition Grant (202203003ETG)。
文摘With the projected global surge in hydrogen demand, driven by increasing applications and the imperative for low-emission hydrogen, the integration of machine learning(ML) across the hydrogen energy value chain is a compelling avenue. This review uniquely focuses on harnessing the synergy between ML and computational modeling(CM) or optimization tools, as well as integrating multiple ML techniques with CM, for the synthesis of diverse hydrogen evolution reaction(HER) catalysts and various hydrogen production processes(HPPs). Furthermore, this review addresses a notable gap in the literature by offering insights, analyzing challenges, and identifying research prospects and opportunities for sustainable hydrogen production. While the literature reflects a promising landscape for ML applications in hydrogen energy domains, transitioning AI-based algorithms from controlled environments to real-world applications poses significant challenges. Hence, this comprehensive review delves into the technical,practical, and ethical considerations associated with the application of ML in HER catalyst development and HPP optimization. Overall, this review provides guidance for unlocking the transformative potential of ML in enhancing prediction efficiency and sustainability in the hydrogen production sector.
基金supported in part by National Natural Science Foundation of China(Nos.52176087 and 52277164)Foundation for Innovative Research Groups of National Natural Science Foundation of China(No.51721004)+1 种基金Scientific Research Program Funded by Shaanxi Provincial Education Department(No.23JP115)Youth Innovation Team of Shaanxi Universities,in part by the Natural Science Basic Research Plan of Shaanxi Province(Nos.2021J Z-48 and 2020JM-462).
文摘Electron emission plays a dominant role in plasma-cathode interactions and is a key factor in many plasma phenomena and industrial applications.It is necessary to illustrate the various electron emission mechanisms and the corresponding applicable description models to evaluate their impacts on discharge properties.In this study,detailed expressions of the simplified formulas valid for field emission to thermo-field emission to thermionic emission typically used in the numerical simulation are proposed,and the corresponding application ranges are determined in the framework of the Murphy-Good theory,which is commonly regarded as the general model and to be accurate in the full range of conditions of the validity of the theory.Dimensionless parameterization was used to evaluate the emission current density of the Murphy-Good formula,and a deviation factor was defined to obtain the application ranges for different work functions(2.5‒5 eV),cathode temperatures(300‒6000 K),and emitted electric fields(10^(5) to 10^(10) V·m^(-1)).The deviation factor was shown to be a nonmonotonic function of the three parameters.A comparative study of particle number densities in atmospheric gas discharge with a tungsten cathode was performed based on the one-dimensional implicit particle-in-cell(PIC)with the Monte Carlo collision(MCC)method according to the aforementioned application ranges.It was found that small differences in emission current density can lead to variations in the distributions of particle number density due to changes in the collisional environment.This study provides a theoretical basis for selecting emission models for subsequent numerical simulations.
基金supported by Shanghai Artificial Intelligence Laboratory.
文摘This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path.Our approach is particularly suitable for high-frequency data.To formulate the parameter estimators,we introduce a theory of pathwise Itôintegrals with respect to fractional Brownian motion.By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes,we demonstrate that our estimators are strongly consistent and pathwise stable.Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings,and may have practical implications for fields including finance,economics,and engineering.
基金Technology Development Program of Jilin Province(YDZJ202201ZYTS640)the National Key Research and Development Program of China(2022YFB4200400)funded by MOST+4 种基金the National Natural Science Foundation of China(52172048 and 52103221)Shandong Provincial Natural Science Foundation(ZR2021QB024 and ZR2021ZD06)Guangdong Basic and Applied Basic Research Foundation(2023A1515012323,2023A1515010943,and 2024A1515010023)the Qingdao New Energy Shandong Laboratory open Project(QNESL OP 202309)the Fundamental Research Funds of Shandong University.
文摘Recently published in Joule,Feng Liu and colleagues from Shanghai Jiaotong University reported a record-breaking 20.8%power conversion efficiency in organic solar cells(OSCs)with an interpenetrating fibril network active layer morphology,featuring a bulk p-in structure and proper vertical segregation achieved through additive-assisted layer-by-layer deposition.This optimized hierarchical gradient fibrillar morphology and optical management synergistically facilitates exciton diffusion,reduces recombination losses,and enhances light capture capability.This approach not only offers a solution to achieving high-efficiency devices but also demonstrates the potential for commercial applications of OSCs.
基金funded by the Science and Technology Innovation Program of Hunan Province(2022RC1224,2022ZYC010)the Changsha Science and Technology Program(kh2004018)the Training Program for Excellent Young Innovators of Changsha(kq2206064)。
文摘Polygonati rhizoma is often used in Chinese medicine and as food.In this study,atmospheric pressure matrixassisted laser desorption ionization and quadruple-time-of-flight(MALDI-Q-TOF)mass spectrometry techniques were applied to P.rhizoma samples from Polygonatum cyrtonema Hua species.Positive ions were mainly detected in the mass range of m/z 200-600,while negative ions were mainly observed in the mass range of m/z 100-450.A total of 263 components were identified and the spatial distribution and changes in saccharides contents during the steaming process of P.rhizoma were investigated.Monosaccharide and disaccharide exhibit a relatively uniform distribution,while the oligosaccharides were mainly found in the bast of fresh P.rhizoma.Although the contents of monosaccharide and disaccharide were increased during steaming,that of trisaccharide,tetrasaccharide,and pentasaccharide were decreased.We used the 5 saccharide types with the greatest variation in content as variables for the principal component analysis(PCA)and cluster analysis.Both PCA and cluster analysis showed that these 5 saccharides can be used as markers in the steaming process of the P.rhizoma.Present study of mass spectrometry imaging provides novel insights into the spatiotemporal accumulation patterns of saccharides in P.rhizoma,improving our understanding of the steaming process.
文摘This study focused on the production of polypropylene(PP)/silver(Ag)composites via additive manufacturing.This study aimed to enhance the quality of medical-grade PP in material extrusion(MEX)three-dimensional printing(3DP)by improving its mechanical properties while simultaneously adding antibacterial properties.The latter can find extremely important and versatile properties that are applicable in defense and security domains.PP/Ag nanocomposites were prepared using a novel method based on a reaction occurring while mixing appropriate quantities of the starting polymers and additives,namely polyvinylpyrrolidone(PVP)as the matrix material and silver nitrate(AgNO_(3))as the filler.This process produced three-dimensional(3D)printed filaments,which were then used to create specimens for a series of standardized tests.It was found that the mechanical properties of the nanocomposites were enhanced in relation to pristine PP,especially for the PP matrix with various loadings of AgNO_(3)and PVP,such as 5.0 wt%and 2.5 wt%,respectively.The voids,inclusions,and actual-to-nominal dimensions also showed improved results.The 3DP specimens exhibited a more effective biocidal performance against Staphylococcus aureus than Escherichia coli,which developed an inhibition zone only in the case of PP with filler loading percentages of AgNO_(3)and PVP at 10.0 wt%and 5.0 wt%,respectively Compounds possessing such properties can be beneficial for various applications requiring increased mechanical properties and biocidal capabilities,such as in the Defence or medical industries.
文摘A new structure with the special property that catastrophes is imposed to ordinary Birth_Death processes is considered. The necessary and sufficient conditions of stochastically monotone, Feller and symmetric properties for the extended birth_death processes with catastrophes are obtained.
基金This work was supported in part by the National Natural Science Foundation of China (10071058, 70273029) the Ministry of Education of China.
文摘This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.
基金Supported by the National Natural Science Foundation of China.
文摘In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform Holder condition, and obtain the uniform packing dimension of multiparameter stable processes. If Z is a stable （N, d, α）-process and αN ≤ d, then the following holds with probability 1 Dim Z（E）=α Dim E for any Borel setE ∈B（R ＋^N）, where Z（E）={x：E←t∈E,Z（t）=x}, Dim （E） denotes the packing dimension of E.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.71871171,71871173,and 71832010)
文摘One of the assumptions of previous research in evolutionary game dynamics is that individuals use only one rule to update their strategy. In reality, an individual's strategy update rules may change with the environment, and it is possible for an individual to use two or more rules to update their strategy. We consider the case where an individual updates strategies based on the Moran and imitation processes, and establish mixed stochastic evolutionary game dynamics by combining both processes. Our aim is to study how individuals change strategies based on two update rules and how this affects evolutionary game dynamics. We obtain an analytic expression and properties of the fixation probability and fixation times(the unconditional fixation time or conditional average fixation time) associated with our proposed process. We find unexpected results. The fixation probability within the proposed model is independent of the probabilities that the individual adopts the imitation rule update strategy. This implies that the fixation probability within the proposed model is equal to that from the Moran and imitation processes. The one-third rule holds in the proposed mixed model. However, under weak selection, the fixation times are different from those of the Moran and imitation processes because it is connected with the probability that individuals adopt an imitation update rule. Numerical examples are presented to illustrate the relationships between fixation times and the probability that an individual adopts the imitation update rule, as well as between fixation times and selection intensity. From the simulated analysis, we find that the fixation time for a mixed process is greater than that of the Moran process, but is less than that of the imitation process. Moreover, the fixation times for a cooperator in the proposed process increase as the probability of adopting an imitation update increases; however, the relationship becomes more complex than a linear relationship.
