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The first rendezvous time of Brownian motion and compound Poisson-type processes
Published online by Cambridge University Press: 14 July 2016
Abstract
The ‘rendezvous time’ of two stochastic processes is the first time at which they cross or hit each other. We consider such times for a Brownian motion with drift, starting at some positive level, and a compound Poisson process or a process with one random jump at some random time. We also ask whether a rendezvous takes place before the Brownian motion hits zero and, if so, at what time. These questions are answered in terms of Laplace transforms for the underlying distributions. The analogous problem for reflected Brownian motion is also studied.
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- Copyright © Applied Probability Trust 2004
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