A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time
Keyword(s):
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 functionP(x,t)of finding the walker at positionxat timetis completely determined by the Laplace transform of the probability density functionφ(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.
2012 ◽
Vol 45
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pp. 195002
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2015 ◽
Vol 93
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pp. 330-339
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2018 ◽
Vol 57
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pp. 439-448
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1999 ◽
Vol 59
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pp. 15374-15380
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2019 ◽
Vol 12
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pp. 1950076
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2016 ◽
Vol 50
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pp. 034002
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