| Invariant Measure for the Markov Process Corresponding to a PDE System |
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| 引用本文： | Fu Bao XI. Invariant Measure for the Markov Process Corresponding to a PDE System[J]. 数学学报(英文版), 2005, 21(3): 457-464. DOI: 10.1007/s10114-004-0510-4 |
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| 作者姓名： | Fu Bao XI |
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| 作者单位： | Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China |
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| 基金项目： | Partially supported by the National Natural Science Foundation of China,Grant No.19901001. Acknowledgements I would like to thank Prof. Chen Mu-Fa for bringing reference [10] to my attention. I would also like to thank the referee for useful comments and suggestions. |
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| 摘 要： | In this paper, we consider the Markov process （X^∈（t）, Z^∈（t）） corresponding to a weakly coupled elliptic PDE system with a small parameter ∈ 〉 0. We first prove that （X^∈（t）, Z^∈（t）） has the Feller continuity by the coupling method, and then prove that （X^∈（t）, Z^∈（t）） has an invariant measure μ^∈（·） by the Foster-Lyapunov inequality. Finally, we establish a large deviations principle for μ^∈（·） as the small parameter e tends to zero.
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| 关 键 词： | Markov过程 不变量测量 椭圆PED系统 连贯性 Foster-Lyapunov不等式 |
| 收稿时间： | 2001-10-26 |
| 修稿时间： | 2001-10-262003-06-24 |
Invariant Measure for the Markov Process Corresponding to a PDE System |
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| Fu Bao Xi. Invariant Measure for the Markov Process Corresponding to a PDE System[J]. Acta Mathematica Sinica(English Series), 2005, 21(3): 457-464. DOI: 10.1007/s10114-004-0510-4 |
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| Authors: | Fu Bao Xi |
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| Affiliation: | (1) Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China |
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| Abstract: | In this paper, we consider the Markov process (X∈(t), Z∈(t)) corresponding to a weakly coupled elliptic PDE system with a small parameter ∈ > 0. We first prove that (X∈(t), Z∈(t)) has the Feller continuity by the coupling method, and then prove that (X∈(t), Z∈ t)) has an invariant measure μ∈(·) by the Foster–Lyapunov inequality. Finally, we establish a large deviations principle for μ∈(·) as the small parameter ∈ tends to zero. Partially supported by the National Natural Science Foundation of China, Grant No. 19901001 |
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| Keywords: | Feller continuity Coupling Invariant measure Foster-Lyapunov inequality Large deviations |
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