Tempered fractional Feynman-Kac equation: Theory and examples.
Tempered fractional Feynman-Kac equation: Theory and examples.
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DOI：
10.1103/physreve.93.032151
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发表时间：
2016-01
期刊：
影响因子：
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通讯作者：
Xiaochao Wu;W. Deng;E. Barkai
中科院分区：
文献类型：
--
作者：
Xiaochao Wu;W. Deng;E. Barkai
布朗运动和非布朗运动的泛函有着广泛的应用，引起了科学家们的极大兴趣。本文着重推导了描述时空回火反常扩散泛函分布的前向和后向分数阶Feynman-Kac方程，该方程属于连续时间随机游走类。显式处理的泛函的几个例子，包括在半空间中的占领时间，第一次通过时间，最大位移，占领分数的波动，和时间平均位置的波动。
Functionals of Brownian and non-Brownian motions have diverse applications and attracted a lot of interest among scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.