Abstract
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 $\varepsilon > 0$. In the present paper 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.
Citation
Alexander Eizenberg. Mark Freidlin. "Large Deviations for Markov Processes Corresponding to PDE Systems." Ann. Probab. 21 (2) 1015 - 1044, April, 1993. https://doi.org/10.1214/aop/1176989280
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