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On Markov Processes with Random Starting Time
- Source :
- Ann. Probab. 1, no. 2 (1973), 223-230
- Publication Year :
- 1973
- Publisher :
- Institute of Mathematical Statistics, 1973.
-
Abstract
- 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.
- Subjects :
- Cauchy problem
Statistics and Probability
Pure mathematics
Semigroup of kernels
Markov kernel
Markov chain
Variable-order Markov model
Markov process
Markov model
Time reversibility
Combinatorics
symbols.namesake
60.69
Markov renewal process
symbols
60.60
Perturbation theory for Markov processes
Markov property
Statistics, Probability and Uncertainty
Mathematics
Subjects
Details
- ISSN :
- 00911798
- Volume :
- 1
- Database :
- OpenAIRE
- Journal :
- The Annals of Probability
- Accession number :
- edsair.doi.dedup.....7a27a5f81aeb8e5c00cb14e0a6c46339