Large deviation principle for a stochastic process with random reinforced relocations

Abstract Stochastic processes with random reinforced relocations have been introduced in a series of papers by Boyer and co-authors (Boyer Solis Salas 2014, Pineda 2016, Boyer, Evans Majumdar 2017) to model animal foraging behaviour. Such process evolves as Markov process, except at relocation times, when it chooses time its whole past according some ‘memory kernel’, jumps value that time. We prove quenched large deviation principle for the times. The difficulty proving this result comes from fact is not Markovian due relocations. Furthermore, inter-relocation times act environment.