Investigation on the properties of Sine-Wiener noise and its induced escape in the particular limit case $D \to \infty$

TL;DR

This paper explores the properties of Sine-Wiener noise as its parameter D approaches infinity, revealing similarities with Wiener processes and analyzing its effects on escape behaviors in stochastic systems.

Contribution

It introduces a new characterization of Sine-Wiener noise's intensity and compares its escape dynamics to Gaussian noise in double-well and Maier-Stein systems.

Findings

SW noise integral resembles Wiener process

Escape times follow Arrhenius law under SW noise

Quasi-potential and exit distributions are similar to Gaussian noise

Abstract

Sine-Wiener noise is increasingly adopted in realistic stochastic modeling for its bounded nature. However, many features of the SW noise are still unexplored. In this paper, firstly, the properties of the SW noise and its integral process are explored as the parameter $D$ in the SW noise tends to infinite. It is found that although the distribution of the SW noise is quite different from Gaussian white noise, the integral process of the SW noise shows many similarities with the Wiener process. Inspired by the Wiener process, which uses the diffusion coefficient to denote the intensity of the Gaussian noise, a quantity is put forward to characterize the SW noise's intensity. Then we apply the SW noise to a one-dimensional double-well potential system and the Maier-Stein system to investigate the escape behaviors. A more interesting result is observed that the mean first exit time also follows the well-known Arrhenius law as in the case of the Gaussian noise, and the quasi-potential and the exit location distributions are very close to the results of the Gaussian noise.