Abstract
We consider a generalized Poisson process with reflection at the level T > 0. Under certain conditions on the distribution of the values of positive jumps of the process, we obtain representations for the characteristic functions of functionals associated with the exit of the indicated process to the negative semiaxis.
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V. S. Korolyuk, Boundary-Value Problems for Complicated Poisson Processes [in Russian], Naukova Dumka, Kiev (1975).
A. A. Borovkov, Stochastic Processes in Queuing Theory [in Russian], Nauka, Moscow (1972).
V. S. Korolyuk, “Boundary-value problems for a complicated Poisson process,” Teor. Ver. Primen., 19, No. 1, 3–14 (1974).
N. S. Bratiichuk and D. V. Gusak, Boundary-Value Problems for Processes with Independent Increments [in Russian], Naukova Dumka, Kiev (1990).
N. S. Bratiichuk, “On the resolvent of a terminated process with independent increments,” Ukr. Mat. Zh., 30, No. 1, 96–100 (1978).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1465–1475, November, 2005.
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Bratiichuk, M.S., Lukovych, O.V. Ruin problem for a generalized Poisson process with reflection. Ukr Math J 57, 1712–1725 (2005). https://doi.org/10.1007/s11253-006-0025-5
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DOI: https://doi.org/10.1007/s11253-006-0025-5