Open Access
April, 1973 On Markov Processes with Random Starting Time
Talma Leviatan
Ann. Probab. 1(2): 223-230 (April, 1973). DOI: 10.1214/aop/1176996975


The paper deals with Markov processes which have both random starting and terminal times. Such processes were suggested by G. A. Hunt, were constructed by L. L. Helms (under the name Markov processes with creation and annihilation) and were treated also by M. Nagasawa and the author. The paper contains a new existence proof by a way of constructing such a process from its given associated semigroup of kernels $\tilde{P}_t, t \geqq 0$, and its (Markov) transition function. This construction is more general than that given by L. L. Helms (in terms of the Markov transition function and the creation measure) and is also more convenient as far as perturbation theory of Markov processes is concerned. Indeed more general relations between this theory and creation of mass processes are established. Finally an application to solving the Cauchy problem in partial differential equations is indicated.


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Talma Leviatan. "On Markov Processes with Random Starting Time." Ann. Probab. 1 (2) 223 - 230, April, 1973.


Published: April, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0263.60030
MathSciNet: MR359018
Digital Object Identifier: 10.1214/aop/1176996975

Keywords: 60.60 , 60.69 , Cauchy problem , Perturbation theory for Markov processes , Semigroup of kernels

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 2 • April, 1973
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