Invariant Measure for the Markov Process Corresponding to a PDE System  

作　　者：Fu Bao XI 

机构地区：[1]Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2005年第3期457-464,共8页数学学报（英文版）

基　　金：the National Natural Science Foundation of China, Grant No. 19901001

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.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.

关 键 词：Feller continuity Coupling Invariant measure Foster-Lyapunov inequality Large deviations 

分 类 号：O211.62[理学—概率论与数理统计]