Chen Yaming, Just Wolfram
School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042102. doi: 10.1103/PhysRevE.90.042102. Epub 2014 Oct 1.
We investigate piecewise-linear stochastic models with regard to the probability distribution of functionals of the stochastic processes, a question that occurs frequently in large deviation theory. The functionals that we are looking into in detail are related to the time a stochastic process spends at a phase space point or in a phase space region, as well as to the motion with inertia. For a Langevin equation with discontinuous drift, we extend the so-called backward Fokker-Planck technique for non-negative support functionals to arbitrary support functionals, to derive explicit expressions for the moments of the functional. Explicit solutions for the moments and for the distribution of the so-called local time, the occupation time, and the displacement are derived for the Brownian motion with dry friction, including quantitative measures to characterize deviation from Gaussian behavior in the asymptotic long time limit.
我们研究分段线性随机模型，涉及随机过程泛函的概率分布，这是大偏差理论中经常出现的一个问题。我们详细研究的泛函与随机过程在相空间点或相空间区域所花费的时间以及惯性运动有关。对于具有不连续漂移的朗之万方程，我们将所谓的用于非负支撑泛函的反向福克 - 普朗克技术扩展到任意支撑泛函，以推导泛函矩的显式表达式。我们推导了具有干摩擦的布朗运动的矩以及所谓局部时间、占据时间和位移分布的显式解，包括在渐近长时间极限下表征偏离高斯行为的定量度量。
