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

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.

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

References in corpus (3)

• First-passage times in complex scale-invariant media
• Bidimensional intermittent search processes: an alternative to Levy flights strategies
• Mean first-passage times of non-Markovian random walkers in confinement

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