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MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM 被引量:5
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作者 吴臻 消华 《Acta Mathematica Scientia》 SCIE CSCD 2010年第5期1819-1836,共18页
In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument... In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth. 展开更多
关键词 backward stochastic differential equations comparison theorem local time
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FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERAL MARTINGALE 被引量:1
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作者 李娟 《Acta Mathematica Scientia》 SCIE CSCD 2006年第3期443-450,共8页
The article first studies the fully coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with the continuous local martingale. The article is mainly divided into two parts. In the first part, it consi... The article first studies the fully coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations (BSDEs) with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale. It is proved that their solutions exist and are unique under the monotonicity conditions. 展开更多
关键词 backward stochastic differential equations local martingale predictable representation property of martingale
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GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS 被引量:1
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作者 李俊松 米超 +1 位作者 邢传智 赵德豪 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2234-2262,共29页
In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The firs... In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner. 展开更多
关键词 refected backward stochastic differential equations forward-backward stochastic diferential equations comparison theorem Wasserstein metric MEAN-FIELD
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FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH STOPPING TIME 被引量:2
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作者 吴臻 《Acta Mathematica Scientia》 SCIE CSCD 2004年第1期91-99,共9页
The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also pr... The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved. 展开更多
关键词 Forward-backward stochastic differential equations stopping time comparison theorem
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A Limit Theorem for Solutions of Backward Stochastic Differential Equations
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作者 BAI Shan HE Jiao 《Journal of China University of Mining and Technology》 2005年第3期271-274,共4页
A limit theorem for solutions of backward stochastic differential equations was established. It extends aresult of Briand et al.
关键词 backward stochastic differential equation GENERATOR converse comparison theorem
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REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LéVY INFINITE 被引量:1
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作者 Lamine SYLLA 《Acta Mathematica Scientia》 SCIE CSCD 2019年第3期819-844,共26页
We consider the problem of viscosity solution of integro-partial differential equation( IPDE in short) with one obstacle via the solution of reflected backward stochastic dif ferential equations(RBSDE in short) with j... We consider the problem of viscosity solution of integro-partial differential equation( IPDE in short) with one obstacle via the solution of reflected backward stochastic dif ferential equations(RBSDE in short) with jumps. We show the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not monotonous and Levy's measure is infinite. 展开更多
关键词 Integro-partial differential equation reflected stochastic differential equations with JUMPS viscosity solution NON-LOCAL operator
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A General Converse Comparison Theorem for Backward Stochastic Differential Equation with Non-lipschitz Coefficient
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作者 LU Min WANG Zeng-wu 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第4期568-573,共6页
In this article, we first introduce g-expectation via the solution of backward stochastic differential equation(BSDE in short) with non-Lipschitz coefficient, and give the properties of g-expectation, then we establ... In this article, we first introduce g-expectation via the solution of backward stochastic differential equation(BSDE in short) with non-Lipschitz coefficient, and give the properties of g-expectation, then we establish a general converse comparison theorem for backward stochastic differential equation with non-Lipschitz coefficient. 展开更多
关键词 backward stochastic differential equation with non-Lipschitz coefficient GENERATOR G-EXPECTATION converse comparison theorem.
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SOME RECENT PROGRESS ON STOCHASTIC HEAT EQUATIONS 被引量:2
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作者 Yaozhong HU 《Acta Mathematica Scientia》 SCIE CSCD 2019年第3期874-914,共41页
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc... This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution. 展开更多
关键词 Gaussian random field Gaussian noise stochastic partial differential equation(stochastic heat equation) Feynman-Kac formula for the solution FeynmanKac formula for the moments of the solution chaos expansion HYPERCONTRACTIVITY moment bounds Holder continuity joint Holder continuity asymptotic behaviour Trotter-Lie formula Skorohod integral
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UNIQUENESS OF VISCOSITY SOLUTIONS OF STOCHASTIC HAMILTON-JACOBI EQUATIONS
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作者 Jinniao QIU Wenning WEI 《Acta Mathematica Scientia》 SCIE CSCD 2019年第3期857-873,共17页
This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the stand... This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity assumptions on the coefficients, the value function is proved to be the unique viscosity solution of the associated stochastic HJ equation. 展开更多
关键词 stochastic HAMILTON-JACOBI equatION optimal stochastic control backward stochastic partial differential equatION viscosity solution
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INVARIANT REPRESENTATION FOR STOCHASTIC DIFFERENTIAL OPERATOR BY BSDES WITH UNIFORMLY CONTINUOUS COEFFICIENTS AND ITS APPLICATIONS
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作者 贾广岩 张娜 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1407-1418,共12页
In this paper, we prove that a kind of second order stochastic differential op- erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of t... In this paper, we prove that a kind of second order stochastic differential op- erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated solutions of BSDEs. Moreover, we give a new proof about g-convexity. 展开更多
关键词 backward stochastic differential equations stochastic differential operators representation theorems converse comparison theorem
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STOCHASTIC DIFFERENTIAL UTILITY UNDER NON-LIPSCHITZ CONDITIONS
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作者 周少甫 王湘君 《Acta Mathematica Scientia》 SCIE CSCD 2000年第4期476-484,共9页
In this paper, the theory of stochastic differential utility is studied. Sufficient conditions for existence, uniqueness, continuity, monotonicity, time consistency, risk aversion and concavity are gived under non-Li... In this paper, the theory of stochastic differential utility is studied. Sufficient conditions for existence, uniqueness, continuity, monotonicity, time consistency, risk aversion and concavity are gived under non-Lipschtz assumptions. 展开更多
关键词 backward stochastic differential equation recursive utility stochastic differential utility utility function
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RANDOM ATTRACTORS FOR A STOCHASTIC HYDRODYNAMICAL EQUATION IN HEISENBERG PARAMAGNET 被引量:4
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作者 郭柏灵 郭春晓 蒲学科 《Acta Mathematica Scientia》 SCIE CSCD 2011年第2期529-540,共12页
This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in H1.
关键词 stochastic partial differential equations Heisenberg paramagnet Randomattractor
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STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE:EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY 被引量:1
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作者 刘俊峰 Ciprian A.TUDOR 《Acta Mathematica Scientia》 SCIE CSCD 2017年第6期1545-1566,共22页
In this paper we study a fractional stochastic heat equation on Rd (d 〉 1) with additive noise /t u(t, x) = Dα/δ u(t, x)+ b(u(t, x) ) + WH (t, x) where D α/δ is a nonlocal fractional differential... In this paper we study a fractional stochastic heat equation on Rd (d 〉 1) with additive noise /t u(t, x) = Dα/δ u(t, x)+ b(u(t, x) ) + WH (t, x) where D α/δ is a nonlocal fractional differential operator and W H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d = 1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus. 展开更多
关键词 stochastic partial differential equation fractional Brownian motion Malliavincalculus Gaussian density estimates
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EFFECTIVE DYNAMICS OF A COUPLED MICROSCOPIC-MACROSCOPIC STOCHASTIC SYSTEM 被引量:2
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作者 任剑 付红波 +1 位作者 曹道民 段金桥 《Acta Mathematica Scientia》 SCIE CSCD 2010年第6期2064-2076,共13页
A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriat... A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence. 展开更多
关键词 microscopic-macroscopic system stochastic partial differential equations averaging principle effective dynamics slow-fast scales
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MAXIMUM PRINCIPLE FOR STOCHASTIC OPTIMAL CONTROL PROBLEM WITH DISTRIBUTED DELAYS 被引量:1
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作者 Qixia ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2021年第2期437-449,共13页
This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables... This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem. 展开更多
关键词 Distributed delay generalized anticipated backward stochastic differential equations optimal control maximum principle
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A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H_2/H_∞ CONTROL WITH RANDOM JUMPS
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作者 张启侠 孙启良 《Acta Mathematica Scientia》 SCIE CSCD 2015年第2期348-358,共11页
A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary an... A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps. 展开更多
关键词 Nonzero-sum stochastic differential games maximum principle Poisson process stochastic H2/H∞ control forward backward stochastic differential equations
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Exact Solutions of the Wick-typ e KdV-Burgers Equation
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作者 LIU Shao-qing GAO Guo-cheng 《Chinese Quarterly Journal of Mathematics》 2016年第2期139-146,共8页
In this paper,we consider the wick-type Kd V-Burgers equation with variable coefficients. By using Tanh method with the aid of Hermite transformation, we deduce the exact solutions which include hyperbolic-exponential... In this paper,we consider the wick-type Kd V-Burgers equation with variable coefficients. By using Tanh method with the aid of Hermite transformation, we deduce the exact solutions which include hyperbolic-exponential, trigonometric-exponential and exponential function solutions for the considered equation. 展开更多
关键词 stochastic partial differential equation Tanh method exact solutions
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含椭圆算子的反射随机偏微分方程
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作者 钱鸿超 李睿智 +1 位作者 桂业伟 彭君 《数学理论与应用》 2024年第1期16-30,共15页
本文考虑一类含椭圆算子的多维反射随机偏微分方程,其解被限制在一个有界凸区域内.本文将利用惩罚法建立其解的存在唯一性定理.
关键词 随机偏微分方程 反射 惩罚法 凸区域 椭圆算子
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EXPONENTIAL CONVERGENCE FOR NONLINEAR SPDES WITH DOUBLE REFLECTING WALLS
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作者 Dengdi CHEN Yan ZHENG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第6期2465-2484,共20页
The present article is devoted to nonlinear stochastic partial differential equations with double reflecting walls driven by possibly degenerate,multiplicative noise.We prove that the corresponding Markov semigroup po... The present article is devoted to nonlinear stochastic partial differential equations with double reflecting walls driven by possibly degenerate,multiplicative noise.We prove that the corresponding Markov semigroup possesses an exponentially attracting invariant measure through asymptotic coupling,in which Foias-Prodi estimation and the truncation technique are crucial for the realization of the Girsanov transform. 展开更多
关键词 stochastic partial differential equations with double reflecting walls exponential mixing asymptotic coupling Girsanov transform
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多维带跳倒向双重随机微分方程解的性质 被引量:7
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作者 孙晓君 卢英 《应用概率统计》 CSCD 北大核心 2008年第1期73-82,共10页
本文研究一类多维带跳倒向双重随机微分方程,给出了It(?)公式在带跳倒向双重随机积分情形下的推广形式,同时运用推广形式的It(?)公式,在Lipschitz条件下证明了方程解的存在性和唯一性。
关键词 带跳倒向双重随机微分方程 伊藤公式 存在性 唯一性
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