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

Mark I. Freidlin; Richard B. Sowers

doi:10.1016/S0304-4149(99)00003-4

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

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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 language	English (US)
Pages (from-to)	23-52
Number of pages	30
Journal	Stochastic Processes and their Applications
Volume	82
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(99)00003-4
State	Published - 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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10.1016/S0304-4149(99)00003-4

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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.",

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T1 - A comparison of homogenization and large deviations, with applications to wavefront propagation

AU - Freidlin, Mark I.

AU - Sowers, Richard B.

PY - 1999/7

Y1 - 1999/7

N2 - 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.

AB - 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.

KW - 35B40

KW - 35K57

KW - 60F10

KW - Homogenization

KW - Huygen's principle

KW - KPP equations

KW - Large deviations

KW - Minkowski geometry

KW - Primary 35B27

KW - Reaction-diffusion equations

KW - Secondary 35K40

KW - Wavefront propagation

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U2 - 10.1016/S0304-4149(99)00003-4

DO - 10.1016/S0304-4149(99)00003-4

M3 - Article

AN - SCOPUS:0042636802

SN - 0304-4149

VL - 82

SP - 23

EP - 52

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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