Moderate deviations for a diffusion-type process in a random environment

P. Chigansky*, R. Liptser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let σ(u), u ∈, be an ergodic stationary Markov chain, taking a finite number of values a1, ⋯ , am, and let b(u) = g(σ(u)), where g is a bounded and measurable function. We consider the diffusion-type process (Mathematic equation present) subject to (Mathematic equation present), where e is a small positive parameter, Bt is a Brownian motion, independent of σ, and κ < 0 is a fixed constant. We show that for κ > (Mathematic equation present), the family (Mathematic equation present) satisfies the large deviation principle (LDP) of Freidlin-Wentzell type with the constant drift b and the diffusion a, given by (Mathematic equation present) where {p1, ⋯ , pm} is the invariant distribution of the chain σ(u).

Original languageAmerican English
Pages (from-to)29-50
Number of pages22
JournalTheory of Probability and its Applications
Volume54
Issue number1
DOIs
StatePublished - 2010

Keywords

  • Diffusion-type processes
  • Freidlin-Wentzell large deviation principle
  • Moderate deviations
  • Random environment

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