A two-sided exit problem for a difference of a compound poisson process and a compound renewal process with a discrete phase space

A two-sided exit problem is solved for a difference of a compound Poisson process and a compound renewal process. The Laplace transforms of the joint distribution of the first exit time, the value of the overshoot, and the value of a linear component at this instant are determined. The results obtained are applied to solve the two-sided exit problem for a particular case of this process, namely, the difference of the compound Poisson process and the renewal process whose jumps are geometrically distributed. The advantage is that these results are in a closed form, in terms of resolvent sequences of the process.

Publication year:2008

Keywords:difference of renewal processes, first exit time, linear component, resolvent sequence, value of the overshoot

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BOF-publication weight:0.1

CSS-citation score:1

Authors:International

Accessibility:Closed