  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.
