Blending Brownian motion and heat equation
Numerical Analysis
2016-06-17 v3 Mathematical Physics
math.MP
Probability
Computational Physics
Abstract
In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with the associated Fokker-Planck equation, which instead describes the evolution of the particle's probability density function. Numerical results show that it is indeed possible to obtain a regularized Brownian motion and a Brownianized heat equation still preserving the global statistical properties of the solutions. The results also suggest that the more macroscale leads the dynamics the more one can reduce the microscopic degrees of freedom.
Keywords
Cite
@article{arxiv.1406.1814,
title = {Blending Brownian motion and heat equation},
author = {Emiliano Cristiani},
journal= {arXiv preprint arXiv:1406.1814},
year = {2016}
}