Large deviations for multi-scale Markovian switching systems with a small diffusion

Article type: Research Article

Authors: He, Qi | Yin, G.^;

Affiliations: Department of Mathematics, University of California, Irvine, CA 92697, USA. E-mail: qhe@math.uci.edu | Department of Mathematics, Wayne State University, Detroit, MI 48202, USA. E-mail: gyin@math.wayne.edu

Note: [] Corresponding author. E-mail: gyin@math.wayne.edu

Abstract: This work develops asymptotic properties of randomly switching and time inhomogeneous dynamic systems under Brownian perturbation with a small diffusion. The switching process is modeled by a continuous-time Markov chain, which portraits discrete events that cannot be modeled by a diffusion process. In the model, there are two small parameters. One of them is ε associated with the generator of the continuous-time, inhomogeneous Markov chain, and the other is δ=δε signifies the small intensity of the diffusion. Assume ε→0 and δε→0 as ε→0. This paper focuses on large deviations type of estimates for such Markovian switching systems with small diffusions. The ratio ε/δε can be a nonzero constant, or equal to 0, or ∞. These three different cases yield three different outcomes. This paper analyzes the three cases and present the corresponding asymptotic properties.

Keywords: large deviations, Markov chain, averaging principle

DOI: 10.3233/ASY-131198

Journal: Asymptotic Analysis, vol. 87, no. 3-4, pp. 123-145, 2014