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

Baghram, Shant; Nikakhtar, Farnik; Tabar, M Reza Rahimi; Rahvar, S; Sheth, Ravi K; Lehnertz, Klaus; Sahimi, Muhammad · Phys Rev E · 2019

basic_science · Level V

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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 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.