Large deviations for multi-scale jump-diffusion processes

TL;DR

This paper derives large deviation principles for a complex two-scale jump-diffusion model with interdependent processes, small noise, and ergodic fast dynamics, extending existing results and illustrating applications in finance and biology.

Contribution

It extends large deviation theory to multi-scale jump-diffusions with interdependence and provides explicit rate functions for practical applications.

Findings

Large deviation principles established for two-scale jump-diffusions.

Explicit large deviation rate functions derived for applications.

Demonstrated relevance to finance and biology models.

Abstract

We obtain large deviation results for a two time-scale model of jump-diffusion processes. The processes on the two time scales are fully inter-dependent, the slow process has small perturbative noise and the fast process is ergodic. Our results extend previous large deviation results for diffusions. We provide concrete examples in their applications to finance and biology, with an explicit calculation of the large deviation rate function.