Invariant Measure for the Markov Process Corresponding to a PDE System

<正> In this paper, we consider the Markov process (X∈（t）, Z∈（t）) corresponding to a weaklycoupled elliptic PDE system with a small parameter∈>0. We first prove that (X∈（t）, Z∈（t）) has theFeller continuity by the coupling method, and then prove that (X∈（t）, Z∈（t）) has an invariant measureμ∈（·） by the Foster-Lyapunov inequality. Finally, we establish a large deviations principle for μ∈（·） asthe small parameter ∈ tends to zero.