Limit theorems for the Wiener process with resetting

TL;DR

This paper develops a large deviation framework for Wiener processes with random resets, providing insights into their rare event behavior and supremum distribution over extended periods.

Contribution

It introduces a large deviation principle for Wiener processes with Poisson resets, including the rate function and supremum behavior, advancing understanding of stochastic processes with resets.

Findings

Established a large deviation principle for reset Wiener processes.

Identified the rate function governing the process deviations.

Derived large deviation results for the process supremum.

Abstract

We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate function and establish a large deviation principle for the supremum of the process over long time intervals.