## Abstract

Let σ(u), u ∈, be an ergodic stationary Markov chain, taking a finite number of values a1, ⋯ , a_{m}, 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, B_{t} 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, ⋯ , p_{m}} is the invariant distribution of the chain σ(u).

Original language | American English |
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Pages (from-to) | 29-50 |

Number of pages | 22 |

Journal | Theory of Probability and its Applications |

Volume | 54 |

Issue number | 1 |

DOIs | |

State | Published - 2010 |

## Keywords

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