论文标题
低细胞性和随机微分方程的Mori-Zwanzig公式
Hypoellipticity and the Mori-Zwanzig formulation of stochastic differential equations
论文作者
论文摘要
我们对有效的Mori-Zwanzig（EMZ）方程进行了彻底的数学分析，该方程是由乘法性高斯白噪声驱动的随机微分方程中噪声平均可观察力的动力学的。在最近对低纤维化操作员的工作的基础上，我们证明了EMZ内存内核和波动术语在及时迅速地收集到一个独特的平衡状态，该状态承认明确表示。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兰格文动力学。
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.
