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Large deviations for Markov processes with resetting.

Research paper by Janusz M JM Meylahn, Sanjib S Sabhapandit, Hugo H Touchette

Indexed on: 15 Jan '16Published on: 15 Jan '16Published in: Physical review. E, Statistical, nonlinear, and soft matter physics



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.