Eizenberg, Alexander; Freidlin, Mark Large deviations for Markov processes corresponding to PDE systems. (English) Zbl 0776.60037 Ann. Probab. 21, No. 2, 1015-1044 (1993). 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. Cited in 3 ReviewsCited in 14 Documents 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 Keywords:small random perturbations; singular perturbations; asymptotic behavior of Markov processes; small parameter; large deviations; Dirichlet problems PDFBibTeX XMLCite \textit{A. Eizenberg} and \textit{M. Freidlin}, Ann. Probab. 21, No. 2, 1015--1044 (1993; Zbl 0776.60037) Full Text: DOI