Non-Gaussian fluctuations in stochastic models with absorbing barriers

TL;DR

This paper analytically characterizes non-Gaussian fluctuations in a one-dimensional stochastic model with an absorbing boundary, extending the van Kampen expansion to capture higher-order effects and matching simulations across all times.

Contribution

It introduces a generalized van Kampen expansion that includes higher-order corrections to accurately describe non-Gaussian fluctuations near absorbing barriers.

Findings

The theory accurately captures non-Gaussian traits of fluctuations.

Analytical solutions match simulation results at all times.

Bridges the gap with previous studies by providing a comprehensive analytical framework.

Abstract

The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order corrections beyond the conventional Gaussian approximation. The theory is shown to successfully capture the non Gaussian traits of the sought distribution returning an excellent agreement with the simulations, for {\it all times} and arbitrarily {\it close} to the absorbing barrier. At large times, a compact analytical solution for the distribution of fluctuations is also obtained, bridging the gap with previous investigations, within the van Kampen picture and without resorting to alternative strategies, as elsewhere hypothesized.