Abstract
A terminating stochastically continuous strictly Markov process is obtained as a result of pasting two nonterminating homogeneous stochastically continuous Markov processes with independent increments, one of which is semicontinuous. It is shown that this process can be extended to a complete homogeneous stochastically continuous strictly Markov Feller process. Previously, this problem has been solved by the author under stronger restrictions-both pasting processes were semicontinuous.
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I. B. Kirichinskaya, “Extension of continuous processes with independent increments,”Ukr. Mat. Zh.,43, No. 9, 1269–1272 (1991).
I. B. Kirichinskaya, “Pasting of two continuous processes with independent increments,”Ukr. Mat. Zh.,43, No. 5, 596–600 (1991).
I. I. Gikhman and A. B. Skorokhod,Theory of Random Processes [in Russian], Vol. 1, Nauka, Moscow (1971).
N. S. Bratiichuk and D. V. Gusak,Boundary-Value Problems for Processes with Independent Increments [in Russian], Naukova Dumka, Kiev (1990).
I. I. Gikhman and A. B. Skorokhod,Theory of Random Processes [in Russian], Vol. 2, Nauka, Moscow (1971).
V. N. Suprun and V. M. Shurenkov, “On the resolvent of a process with independent increments terminating at the moment of transition to the negative semiaxis,” in:Studies in the Theory of Random Processes [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1976), pp. 170–174.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 487–491, April, 1993.
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Kirichinskaya, I.B. Pasting of two processes with independent increments. Ukr Math J 45, 520–525 (1993). https://doi.org/10.1007/BF01062948
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DOI: https://doi.org/10.1007/BF01062948