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Hypoellipticity and the Mori–Zwanzig formulation of stochastic differential equations
Published Web Location
https://pubs.aip.org/aip/jmp/article/62/10/103505/318461/Hypoellipticity-and-the-Mori-Zwanzig-formulationNo data is associated with this publication.
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 that admits an explicit representation. We apply the new theoretical results to the Langevin dynamics of a high-dimensional particle system with smooth interaction potential.
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