Large deviations of Markov chains with multiple time-scales

Abstract

For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a deterministic limit and a central limit theorem around it have already been proven in [16] and [17]. We present here a general approach to proving a large deviation principle in path space for such multi-scale Markov processes. Motivated by models arising in systems biology, we apply these large deviation results to general chemical reaction systems which exhibit multiple time-scales, and provide explicit calculations for several relevant examples.

45 pages (Lemma 3.7 corrected)

References in corpus (2)

• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
• Large deviations for multi-scale jump-diffusion processes

Cited by in corpus (3)

• A large deviation principle for Markovian slow-fast systems
• Large deviations for Markov processes with switching and homogenisation via Hamilton-Jacobi-Bellman equations
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory