Baghram Shant, Nikakhtar Farnik, Tabar M Reza Rahimi, Rahvar S, Sheth Ravi K, Lehnertz Klaus, Sahimi Muhammad
Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran.
Center for Particle Cosmology, University of Pennsylvania, 209 S. 33rd Street, Philadelphia, Pennsylvania 19104, USA.
Phys Rev E. 2019 Jun;99(6-1):062101. doi: 10.1103/PhysRevE.99.062101.
We propose an analytical approach to study non-Markov random walks by employing an exact enumeration method. Using the method, we derive an exact expansion for the first-passage time (FPT) distribution of any continuous differentiable non-Markov random walk with Gaussian or non-Gaussian multivariate distribution. As an example, we study the FPT distribution of the fractional Brownian motion with a Hurst exponent H∈(1/2,1) that describes numerous non-Markov stochastic phenomena in physics, biology, and geology and for which the limit H=1/2 represents a Markov process.
我们提出一种分析方法，通过采用精确枚举法来研究非马尔可夫随机游走。利用该方法，我们推导出了具有高斯或非高斯多元分布的任何连续可微非马尔可夫随机游走的首次通过时间（FPT）分布的精确展开式。作为一个例子，我们研究了赫斯特指数H∈(1/2,1)的分数布朗运动的FPT分布，它描述了物理、生物和地质领域中的许多非马尔可夫随机现象，而极限H = 1/2代表一个马尔可夫过程。
