A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time. (13th March 2014)

• Record Type: Journal Article
• Authors: Shi, Long; Yu, Zuguo; Mao, Zhi; Xiao, Aiguo
• Other Names: Li C. Academic Editor.; Liu F. Academic Editor.; Yuste S. B. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-03-13
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/182508
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P ( x, t ) of finding the walker at position x at time t is completely determined by the Laplace transform of the probability density function φ ( t ) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.