A comparison of homogenization and large deviations, with applications to wavefront propagation

Mark I. Freidlin, Richard B. Sowers

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the combined effects of homogenization and large deviations in a stochastic differential equation. We show that there are three regimes, depending on the relative rates at which the small viscosity parameter and the homogenization parameter tend to zero. We prove some large-deviations-type estimates, and then apply these results to study wavefronts in both a single reaction-diffusion equation and in a system of reaction-diffusion equations.

Original languageEnglish (US)
Pages (from-to)23-52
Number of pages30
JournalStochastic Processes and their Applications
Volume82
Issue number1
DOIs
StatePublished - Jul 1999

Keywords

  • 35B40
  • 35K57
  • 60F10
  • Homogenization
  • Huygen's principle
  • KPP equations
  • Large deviations
  • Minkowski geometry
  • Primary 35B27
  • Reaction-diffusion equations
  • Secondary 35K40
  • Wavefront propagation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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