Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-06-01T21:00:03.158Z Has data issue: false hasContentIssue false
  • English
  • Français

Creation of Mass Processes and Perturbation Theory

Published online by Cambridge University Press:  20 November 2018

Talma Leviatan
Talma Leviatan*
Affiliation:
Tel-Aviv University, Tel-Aviv, Israel
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Creation of mass processes were treated lately by several authors. The idea was to find some generalized Markov process that will correspond to a semigroup of operators which are not necessarily contraction operators (or equivalently to a quasi transition function which is not submarkov). It was G. A. Hunt [6] who first suggested the idea of Markov processes in which both the starting time and the terminal time are random. Such processes were constructed by Helms [4] and treated also by Nagasawa [12] and the author [10].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 456 - 467
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Blumenthal, R. M. and Getoor, R. K., Markov processes and potential theory (Academic Press, New York and London, 1969).Google Scholar
2. Dunford, N. and Schwartz, J., Linear operators. Part I: General theory (Interscience Publication Inc., New York, 1964).Google Scholar
3. Dynkin, E. B., Markov processes. Vol. I (Springer-Verlag, Berlin, 1965).Google Scholar
4. Helms, L. L., Markov processes with creation of mass. I, II; Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1967), 225-234; 15 (1970), 208–218.Google Scholar
5. Hunt, G. A., Markov processes and potentials. II, Illinois J. Math. 1 (1957), 316–369.Google Scholar
6. Hunt, G. A., Markov chains and Martin boundaries, Illinois J. Math. 4 (1960), 313–340.Google Scholar
7. Ikeda, N., Nagasawa, M., and Watanabe, S., Branching Markov processes, Math. Kyoto Univ. 8 (1968), 233-278, 365-410; 9 (1969), 95–160.Google Scholar
8. Ito, K. and Mckean, H. P., Jr., Diffusion processes and their sample path (Springer-Ver lag, Berlin, 1965).Google Scholar
9. Knight, F. B., A path space for positive semigroups, Illinois J. Math. 13 (1969), 542–563.Google Scholar
10. Leviatan, T., Perturbations of Markov processes, J. Functional Analysis 10 (1972), 309–325.Google Scholar
11. Meyer, P. A., Probability and potentials (Blandsdell Pub. 10, Waltham, Mass., 1966).Google Scholar
12. Nagasawa, M., Markov processes with creation and annihilation, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete U (1969), 49-70.Google Scholar
13. Silverstein, M. L., Markov processes with creation of particles, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 9 (1968), 235–257.Google Scholar