TY - JOUR

T1 - Moderate deviations for a diffusion-type process in a random environment

AU - Chigansky, P.

AU - Liptser, R.

PY - 2010

Y1 - 2010

N2 - 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).

AB - 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).

KW - Diffusion-type processes

KW - Freidlin-Wentzell large deviation principle

KW - Moderate deviations

KW - Random environment

UR - http://www.scopus.com/inward/record.url?scp=77749346056&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97983973

DO - 10.1137/S0040585X97983973

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AN - SCOPUS:77749346056

SN - 0040-585X

VL - 54

SP - 29

EP - 50

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

IS - 1

ER -