Stochastic resetting by a random amplitude

TL;DR

This paper generalizes stochastic resetting by allowing the resetting amplitude to be random, enabling partial or overshoot resets, with applications across geophysics, population dynamics, finance, and search processes.

Contribution

It introduces a novel stochastic resetting model with random amplitudes, expanding the scope of resetting strategies in various complex systems.

Findings

Different scenarios of random-amplitude resetting analyzed

Dynamics of the process characterized under various conditions

Potential applications in multiple scientific fields

Abstract

Stochastic resetting, a diffusive process whose amplitude is "reset" to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. We here generalize the resetting step by introducing a random resetting amplitude, such that the diffusing particle may be only partially reset towards the trajectory origin, or even overshoot the origin in a resetting step. We introduce different scenarios for the random-amplitude stochastic resetting process and discuss the resulting dynamics. Direct applications are geophysical layering (stratigraphy) as well as population dynamics or financial markets, as well as generic search processes.