福克尔普朗克方程

S. Loos
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引用次数: 0

摘要

在前一章中,我们介绍了朗之万方程,它在随机水平上描述了本文研究的随机过程。对于马尔可夫系统,众所周知,福克-普朗克方程(FPE)在概率水平上提供了一种互补的描述方式。这些是确定性方程,其解是概率密度函数。下面,我们将简要介绍这个概念,首先关注马尔可夫情况。
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Fokker-Planck Equations
In the preceding chapter, we have introduced the Langevin equation, which describes the random processes studied in this thesis on a stochastic level. For Markovian systems, it is well known that Fokker-Planck equations (FPE) provide a complementary way of description, on the probabilistic level. These are deterministic equations, whose solutions are probability density functions. In the following, we will briefly introduce this concept, first focusing on the Markovian case.
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Infinite Fokker-Planck Hierarchy Markovian Embedding—A New Derivation of the Fokker-Planck Hierarchy Force-Linearization Closure The Langevin Equation Stochastic Thermodynamics
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