English

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

Statistical Mechanics 2019-06-07 v1 Cosmology and Nongalactic Astrophysics Data Analysis, Statistics and Probability

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(1/2,1)H\in(1/2,1) that describes numerous non-Markov stochastic phenomena in physics, biology and geology, and for which the limit H=1/2H=1/2 represents a Markov process.

Keywords

Cite

@article{arxiv.1906.02081,
  title  = {Exact enumeration approach to first-passage time distribution of non-Markov random walks},
  author = {Shant Baghram and Farnik Nikakhtar and M. Reza Rahimi Tabar and Sohrab Rahvar and Ravi K. Sheth and Klaus Lehnertz and Muhammad Sahimi},
  journal= {arXiv preprint arXiv:1906.02081},
  year   = {2019}
}

Comments

23 pages, 4 figures, 1 table and 5 appendices. Published version