Hypoellipticity and the Mori–Zwanzig formulation of stochastic differential equations
Copyright policy )Hypoellipticity and the Mori–Zwanzig formulation of stochastic differential equations
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.
- University of California United States
- University of California, Merced United States
- University of California, Santa Cruz United States
Applied Mathematics, Statistics, Mathematical sciences, Elliptic operators and their generalizations, FOS: Physical sciences, Mathematical Physics (math-ph), Dynamical Systems (math.DS), Langevin dynamics, Mathematical Sciences, Stochastic ordinary differential equations (aspects of stochastic analysis), Physical sciences, Mori-Zwanzig equation, Physical Sciences, FOS: Mathematics, Mathematics - Dynamical Systems, Markov semigroups and applications to diffusion processes, Mathematical Physics
Applied Mathematics, Statistics, Mathematical sciences, Elliptic operators and their generalizations, FOS: Physical sciences, Mathematical Physics (math-ph), Dynamical Systems (math.DS), Langevin dynamics, Mathematical Sciences, Stochastic ordinary differential equations (aspects of stochastic analysis), Physical sciences, Mori-Zwanzig equation, Physical Sciences, FOS: Mathematics, Mathematics - Dynamical Systems, Markov semigroups and applications to diffusion processes, Mathematical Physics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!