Brownian colloidal particles: Ito, Stratonovich or a different stochastic interpretation

TL;DR

This paper investigates the appropriate stochastic interpretation for modeling Brownian colloidal particles, comparing the underdamped Langevin approach with different interpretations and their impact on theoretical and numerical results.

Contribution

It clarifies the relationship between different stochastic interpretations by analyzing the underdamped Langevin equation and its Fokker-Planck form, resolving the interpretation dichotomy.

Findings

Underdamped Langevin equations provide a unified framework.

Numerical simulations align with the Stratonovich interpretation.

The choice of interpretation affects the modeling of multiplicative noise.

Abstract

Recent experiments on Brownian colloidal particles have been studied theoretically in terms of overdamped Langevin equations with multiplicative white noise using an unconventional stochastic interpretation. Complementary numerical simulations of the same system are well described using the conventional Stratonovich interpretation. Here we address this dichotomy from a more generic starting point: the underdamped Langevin equation and its corresponding Fokker--Planck equation.