Summary
We continue the study of exit problems for perturbed random evolution equations corresponding to the weakly coupled elliptic PDE systems. In the present paper we consider the cases where the corresponding random evolutions stay in a given domain for ever with probability one, but do not hinder the exit of the perturbed process. We treat such problems by methods based on the averaging principle. In such a way we also study the asymptotic behavior of the solutions of the corresponding perturbed Dirichlet problems.
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Supported in part by US-Israel BSF
Sponsored in part by the Landau Center for Mathematical Research in Analysis supported by the Minerva Foundation (Federal Republic of Germany)
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Eizenberg, A., Freidlin, M. Averaging principle for perturbed random evolution equations and corresponding Dirichlet problems. Probab. Th. Rel. Fields 94, 335–374 (1993). https://doi.org/10.1007/BF01199248
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DOI: https://doi.org/10.1007/BF01199248
Mathematics Subject Classification (1980)
- 60F10
- 35J55