TY - JOUR
A2 - Droz, Michel
AU - Yamamoto, Ken
PY - 2013
DA - 2013/10/27
TI - Solution and Analysis of a One-Dimensional First-Passage Problem with a Nonzero Halting Probability
SP - 831390
VL - 2013
AB - This paper treats a kind of a one-dimensional first-passage problem, which seeks the probability that a random walker first hits the origin at a specified time. In addition to a usual random walk which hops either rightwards or leftwards, the present paper introduces the “halt” that the walker does not hop with a nonzero probability. The solution to the problem is expressed using a Gauss hypergeometric function. The moment generating function of the hitting time is also calculated, and a calculation technique of the moments is developed. The author derives the long-time behavior of the hitting-time distribution, which exhibits power-law behavior if the walker hops to the right and left with equal probability.
SN - 2356-7112
UR - https://doi.org/10.1155/2013/831390
DO - 10.1155/2013/831390
JF - International Journal of Statistical Mechanics
PB - Hindawi Publishing Corporation
KW -
ER -