Nonstationary Optimal Paths and Tails of Prehistory Probability Density in Multistable Stochastic Systems

TL;DR

This paper investigates the non-Gaussian, asymmetric tails of prehistory probability density in multistable stochastic systems using nonstationary optimal fluctuations, revealing new insights into noise-driven fluctuations and their mathematical descriptions.

Contribution

It introduces a novel analysis of prehistory probability density tails in nonlinear multistable systems using nonstationary optimal fluctuations, linking them to system symmetry properties.

Findings

Prehistory probability density is non-Gaussian and highly asymmetrical.

In systems with detailed balance, it coincides with the transition probability.

Numerical simulations support the theoretical analysis.

Abstract

The tails of prehistory probability density in nonlinear multistable stochastic systems driven by white Gaussian noise, which has been a subject of recent study, are analyzed by employing the concepts of nonstationary optimal fluctuations. Results of numerical simulations evidence that the prehistory probability density is non-Gaussian and highly asymmetrical that is an essential feature of noise driven fluctuations in nonlinear systems. We show also that in systems with the detail balance the prehistory probability density is the conventional transition probability that obeys the backward Kolmogorov equation.