Expediting Feller process with stochastic resetting

TL;DR

This paper investigates how stochastic resetting influences the first-passage times of the Feller process, revealing conditions under which resetting accelerates or decelerates first-passage depending on parameters.

Contribution

It provides an analytical study of Feller diffusion with stochastic resetting, highlighting the impact of boundary positions and parameters on first-passage times.

Findings

Resetting accelerates first-passage for certain parameter regimes.

Critical values of b8 influence the effect of resetting.

The effect depends on the relative position of the boundary and initial point.

Abstract

We explore the effect of stochastic resetting on the first-passage properties of Feller process. The Feller process can be envisioned as space-dependent diffusion, with diffusion coefficient $D(x)=x$, in a potential $U(x)=x\left(\frac{x}{2}-\theta \right)$ that owns a minimum at $\theta$. This restricts the process to the positive side of the origin and therefore, Feller diffusion can successfully model a vast array of phenomena in biological and social sciences, where realization of negative values is forbidden. In our analytically tractable model system, a particle that undergoes Feller diffusion is subject to Poissonian resetting, i.e., taken back to its initial position at a constant rate $r$, after random time epochs. We addressed the two distinct cases that arise when the relative position of the absorbing boundary ($x_a$) with respect to the initial position of the particle ($x_0$) differ, i.e., for (a) $x_0<x_a$ and (b) $x_a<x_0$. We observe that for $x_0<x_a$, resetting accelerates first-passage when $\theta<\theta_c$, where $\theta_c$ is a critical value of $\theta$ that decreases when $x_a$ is moved away from the origin. In stark contrast, for $x_a<x_0$, resetting accelerates first-passage when $\theta>\theta_c$, where $\theta_c$ is a critical value of $\theta$ that increases when $x_0$ is moved away from the origin. Our study opens up the possibility of a series of subsequent works with more case-specific models of Feller diffusion with resetting.