A two-sided exit problem for a difference of a compound Poisson process and a compound renewal process with a discrete phase space
نویسندگان
چکیده
Abstract 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.
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