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Averaging principle for perturbed random evolution equations and corresponding Dirichlet problems
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  • Published: September 1993

Averaging principle for perturbed random evolution equations and corresponding Dirichlet problems

  • Alexander Eizenberg1 &
  • Mark Freidlin2 

Probability Theory and Related Fields volume 94, pages 335–374 (1993)Cite this article

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  • 7 Citations

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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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Author information

Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University, Givat Ram, Jerusalem, Israel

    Alexander Eizenberg

  2. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    Mark Freidlin

Authors
  1. Alexander Eizenberg
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  2. Mark Freidlin
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Additional information

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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  • Received: 08 August 1991

  • Revised: 01 May 1992

  • Issue Date: September 1993

  • DOI: https://doi.org/10.1007/BF01199248

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Mathematics Subject Classification (1980)

  • 60F10
  • 35J55
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