亚椭圆性与随机微分方程的Mori-Zwanzig形式
Hypoellipticity and the Mori-Zwanzig formulation of stochastic differential equations
摘要：
我们开发了一个彻底的数学分析的有效的Mori-Zwanzig（EMZ）方程的噪声平均观测量的动力学在乘性高斯白噪声驱动的随机微分方程。最近的工作的基础上，亚椭圆算子，我们证明了EMZ记忆内核和波动项的时间指数快速收敛到一个独特的平衡态，承认一个明确的表示。我们将新的理论结果应用于具有光滑相互作用势的高维粒子系统的朗之万动力学。
英文摘要：
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.
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