Hypoellipticity and the Mori-Zwanzig formulation of stochastic differential equations
Mathematical Physics
2021-10-27 v3 Dynamical Systems
math.MP
Abstract
We develop a thorough mathematical analysis of the effective Mori-Zwanzig (EMZ) equation governing the dynamics of noise-averaged observables in stochastic differential equations driven by multiplicative Gaussian white noise. Building upon recent work on hypoelliptic operators, we prove that the EMZ memory kernel and fluctuation terms converge exponentially fast in time to a unique equilibrium state which admits an explicit representation. We apply the new theoretical results to the Langevin dynamics of a high-dimensional particle system with smooth interaction potential.
Keywords
Cite
@article{arxiv.2001.04565,
title = {Hypoellipticity and the Mori-Zwanzig formulation of stochastic differential equations},
author = {Yuanran Zhu and Daniele Venturi},
journal= {arXiv preprint arXiv:2001.04565},
year = {2021}
}
Comments
22 pages, 1 figure