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arXiv · 1906.02081

Exact enumeration approach to first-passage time distribution of non-Markov random walks

Shant Baghram·Farnik Nikakhtar·M. Reza Rahimi Tabar·Sohrab Rahvar·Ravi K. Sheth·Klaus Lehnertz·Muhammad Sahimi
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Abstract

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 for any continuous, differentiable non-Markov random walk with Gaussian or non-Gaussian multivariate distribution. As an example, we study the FPT distribution of a fractional Brownian motion with a Hurst exponent $H\in(1/2,1)$ that describes numerous non-Markov stochastic phenomena in physics, biology and geology, and for which the limit $H=1/2$ represents a Markov process.

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Shant Baghram, Farnik Nikakhtar, M. Reza Rahimi Tabar, Sohrab Rahvar, Ravi K. Sheth, Klaus Lehnertz, Muhammad Sahimi. 2019-06-05. Exact enumeration approach to first-passage time distribution of non-Markov random walks. https://doi.org/10.1103/physreve.99.062101

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