Solution and Analysis of a One-Dimensional First-Passage Problem with a Nonzero Halting Probability. (27th October 2013)

• Record Type: Journal Article
• Authors: Yamamoto, Ken
• Other Names: Droz Michel Academic Editor.
• Is Part Of: International journal of statistical mechanics. Volume 2013(2013)
• Publication Date: 2013-10-27
• Subjects: Statistical mechanics -- Periodicals; Statistical mechanics; Periodicals; 530.13
• DOI: 10.1155/2013/831390
• Languages: English
• ISSNs: 2356-7112

Abstract

Abstract : 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.