The author considers the contact process on a branching plane Td×Z, which is the product of a regular tree Td and the line Z. It is shown that above the second critical point, the complete convergence theory holds.
In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we constru...In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.展开更多
Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an ap...Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an application, Marcinkiewicz-Zygmundtype strong law of large numbers for this moving average process is presented in this paper.展开更多
基金Research was supported in part by Grant G1999075106 from the Ministry of Science and Technology of China.
文摘The author considers the contact process on a branching plane Td×Z, which is the product of a regular tree Td and the line Z. It is shown that above the second critical point, the complete convergence theory holds.
基金Supported in part by the NNSF of China (10531070,10625101)the National Basic Research Program of China (2006CB805900)
文摘In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.
基金Supported by the National Natural Science Foundation of China（11501005, 11526033） Supported by the Natural Science Foundation of Anhui Province（1408085QA02, 1508085J06, 1608085QA02）+3 种基金 Supported by the Provincial Natural Science Research Project of Anhui Colleges（KJ2014A020, KJ2015A065） Supported by the Quality Engineering Project of Anhui Province（2015jyxm054） Supported by the Students Science Research Training Program of Anhui University（KYXL2014016, KYXL2014013） Supported by the Applied Teaching Model Curriculum of Anhui University（XJYYKC1401, ZLTS2015053）
文摘Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an application, Marcinkiewicz-Zygmundtype strong law of large numbers for this moving average process is presented in this paper.
