Large deviations for Markov processes with resetting
Abstract
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of time-additive functions or observables of Markov processes with resetting. By deriving a renewal formula linking generating functions with and without resetting we are able to obtain the rate function of such observables, characterizing the likelihood of their fluctuations in the long-time limit. We consider as an illustration the large deviations of the area of the Ornstein-Uhlenbeck process with resetting. Other applications involving diffusions, random walks, and jump processes with resetting or catastrophes are discussed.
Cite
@article{arxiv.1510.02431,
title = {Large deviations for Markov processes with resetting},
author = {Janusz M. Meylahn and Sanjib Sabhapandit and Hugo Touchette},
journal= {arXiv preprint arXiv:1510.02431},
year = {2016}
}
Comments
v1: 7 pages, 3 figures; v2: 8 pages, 3 figures, minor corrections, close to published version