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A note on passage times and infinitely divisible distributions

Published online by Cambridge University Press:  14 July 2016

H. D. Miller*
Affiliation:
Imperial College, London

Extract

Let X(t) be the position at time t of a particle undergoing a simple symmetrical random walk in continuous time, i.e. the particle starts at the origin at time t = 0 and at times T 1, T 1 + T 2, … it undergoes jumps ξ 1, ξ 2, …, where the time intervals T 1, T 2, … between successive jumps are mutually independent random variables each following the exponential density e–t while the jumps, which are independent of the τi , are mutually independent random variables with the distribution . The process X(t) is clearly a Markov process whose state space is the set of all integers.

Information

Type
Short Communications
Copyright
Copyright © Sheffield: Applied Probability Trust 

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