Local large deviation principle for Wiener process with random resetting

TL;DR

This paper establishes a local large deviation principle for Wiener processes with random resettings occurring at Poisson times, where reset points are randomly chosen according to a conditional distribution, relevant in various scientific fields.

Contribution

It introduces the first LLDP for Wiener processes with Poisson-driven random resettings, extending large deviation theory to this class of stochastic processes.

Findings

Proves the LLDP for Wiener processes with random resettings

Characterizes the rate function for the process

Provides a framework applicable to physics, chemistry, biology, and economics

Abstract

We consider a class of Markov processes with resettings, where at random times, the Markov processes are restarted from a predetermined point or a region. These processes are frequently applied in physics, chemistry, biology, economics, and in population dynamics. In this paper we establish the local large deviation principle (LLDP) for the Wiener processes with random resettings, where the resettings occur at the arrival time of a Poisson process. Here, at each resetting time, a new resetting point is selected at random, according to a conditional distribution.