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Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE’s with a small parameter
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  • Published: 03 March 2009

Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE’s with a small parameter

  • M. Freidlin1 &
  • L. Koralov1 

Probability Theory and Related Fields volume 147, pages 273–301 (2010)Cite this article

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Abstract

In this paper, we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes. In particular, we discuss the exit problem and metastability for the processes corresponding to quasi-linear initial-boundary value problems.

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Authors and Affiliations

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

    M. Freidlin & L. Koralov

Authors
  1. M. Freidlin
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  2. L. Koralov
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Corresponding author

Correspondence to M. Freidlin.

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Cite this article

Freidlin, M., Koralov, L. Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE’s with a small parameter. Probab. Theory Relat. Fields 147, 273–301 (2010). https://doi.org/10.1007/s00440-009-0208-8

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  • Received: 05 October 2008

  • Revised: 01 February 2009

  • Published: 03 March 2009

  • Issue Date: May 2010

  • DOI: https://doi.org/10.1007/s00440-009-0208-8

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Keywords

  • Nonlinear perturbations
  • Exit problem
  • Metastability

Mathematics Subject Classification (2000)

  • 60F10
  • 35K55
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