A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time

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 fun...

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Main Authors:	Long Shi, Zuguo Yu, Zhi Mao, Aiguo Xiao
Format:	Article
Language:	English
Published:	Hindawi Limited 2014-01-01
Series:	The Scientific World Journal
Online Access:	http://dx.doi.org/10.1155/2014/182508

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spelling	doaj-8e9297a3da6d4694b631f27f3d6a56e42020-11-24T21:50:57ZengHindawi LimitedThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/182508182508A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting TimeLong Shi0Zuguo Yu1Zhi Mao2Aiguo Xiao3Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, ChinaHunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, ChinaHunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, ChinaHunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, ChinaIn 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.http://dx.doi.org/10.1155/2014/182508
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Long Shi Zuguo Yu Zhi Mao Aiguo Xiao
spellingShingle	Long Shi Zuguo Yu Zhi Mao Aiguo Xiao A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time The Scientific World Journal
author_facet	Long Shi Zuguo Yu Zhi Mao Aiguo Xiao
author_sort	Long Shi
title	A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time
title_short	A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time
title_full	A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time
title_fullStr	A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time
title_full_unstemmed	A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time
title_sort	directed continuous time random walk model with jump length depending on waiting time
publisher	Hindawi Limited
series	The Scientific World Journal
issn	2356-6140 1537-744X
publishDate	2014-01-01
description	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.
url	http://dx.doi.org/10.1155/2014/182508
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A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time

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