Numerical prediction of the steady-state distribution under stochastic resetting from measurements

TL;DR

This paper introduces a numerical renewal method to predict the steady-state distribution of particles under stochastic resetting using measured propagators and resetting time distributions, applicable to complex systems with interactions or environmental memory.

Contribution

It develops a numerical approach that estimates steady states from measured propagators, extending renewal methods to systems where propagators are not analytically known.

Findings

Validated on systems with interacting particles and environmental memory.

Accurately predicts steady-state distributions from measurements.

Applicable to complex real-world systems with unknown propagators.

Abstract

A common and effective method for calculating the steady-state distribution of a process under stochastic resetting is the renewal approach that requires only the knowledge of the reset-free propagator of the underlying process and the resetting time distribution. The renewal approach is widely used for simple model systems such as a freely diffusing particle with exponentially distributed resetting times. However, in many real-world physical systems, the propagator, the resetting time distribution, or both are not always known beforehand. In this study, we develop a numerical renewal method to determine the steady-state probability distribution of particle positions based on the measured system propagator in the absence of resetting combined with the known or measured resetting time distribution. We apply and validate our method in two distinct systems: one involving interacting particles and the other featuring strong environmental memory. Thus, the renewal approach can be used to predict the steady state under stochastic resetting of any system, provided that the free propagator can be measured and that it undergoes complete resetting.