A probabilistic interpretation of a non-conservative and path-dependent nonlinear reaction-advection-diffusion system
Probability
2025-10-14 v2
Abstract
Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a non-Markovian McKean-Vlasov stochastic differential equation coupled with a Feynman-Kac-type equation. We discuss the well-posedness of such a stochastic model, and establish the propagation of chaos property for the associated interacting particle system.
Cite
@article{arxiv.2407.19301,
title = {A probabilistic interpretation of a non-conservative and path-dependent nonlinear reaction-advection-diffusion system},
author = {Daniela Morale and Leonardo Tarquini and Stefania Ugolini},
journal= {arXiv preprint arXiv:2407.19301},
year = {2025}
}