Pasting of two processes with independent increments

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.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 487–491, April, 1993.