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Large deviations for Markov processes corresponding to PDE systems. (English) Zbl 0776.60037

Summary: We continue the study of the asymptotic behavior of Markov processes \((X^ \varepsilon(t),\nu^ \varepsilon(t))\) corresponding to systems of elliptic PDE with a small parameter \(\varepsilon>0\). We consider the case where the process \((X^ \varepsilon(t),\nu^ \varepsilon(t))\) can leave a given domain \(D\) only due to large deviations from the degenerate process \((X^ 0(t),\nu^ 0(t))\). In this way we study the limit behavior of solutions of corresponding Dirichlet problems.

MSC:

60F10 Large deviations
35B25 Singular perturbations in context of PDEs
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
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