Additive functionals of semi-Markov processes with absorption

A. P. Cherenkov


Abstract: Given a semi-Markov process with an arbitrary set of states, a criterion is obtained for the attainability of a certain isolated subset of states and for finiteness of the average attainment time. An equation is given for the average of an additive functional of a process with absorption, existence and uniqueness conditions are deduced for the solution of that equation in a given class of functions, and an integral representation is obtained for the solution.

UDC: 519.2

Received: 18.12.1973

 English version: Mathematical Notes, 1975, 17:2, 189–194

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