title: 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.
authors.affiliation: Mathematical Institute, Leiden University, Leiden, The Netherlands.|Department of Physics, Institute of Theoretical Physics, Stellenbosch University, Stellenbosch 7600, South Africa.
authors.forename: Janusz M
authors.initials: JM
authors.lastname: Meylahn
authors.affiliation: Raman Research Institute, Bangalore 560080, India.
authors.forename: Sanjib
authors.initials: S
authors.lastname: Sabhapandit
authors.affiliation: Department of Physics, Institute of Theoretical Physics, Stellenbosch University, Stellenbosch 7600, South Africa.|National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa.
authors.forename: Hugo
authors.initials: H
authors.lastname: Touchette