http://arxiv.org/abs/1906.02081
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.
S. Baghram, F. Nikakhtar, M. Tabar, et. al.
Fri, 7 Jun 19
46/49
Comments: 23 pages, 4 figures, 1 table and 5 appendices. Published version