A note on passage times and infinitely divisible distributions
- 1 August 1967
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 4 (2) , 402-405
- https://doi.org/10.2307/3212034
Abstract
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 T1, T1 + T2, … it undergoes jumps ξ1, ξ2, …, where the time intervals T1, T2, … 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.Keywords
This publication has 2 references indexed in Scilit:
- Infinitely Divisible Distributions and Bessel Functions Associated with Random WalksSIAM Journal on Applied Mathematics, 1966
- The Use of Green's Functions in the Study of Bounded Random Walks with Application to Queuing TheoryJournal of Mathematics and Physics, 1962