Excessive Measures

R.K. Getoor (Autor)

Buch | Softcover

190 Seiten

2011
Springer-Verlag New York Inc.
978-1-4612-8036-1 (ISBN)

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The study of the cone of excessive measures associated with a Markov process goes back to Hunt's fundamental mem- oir [H57]. However until quite recently it received much less attention than the cone of excessive functions. The fact that an excessive function can be composed with the underlying Markov process to give a supermartingale, subject to secondary finiteness hypotheses, is crucial in the study of excessive func- tions. The lack of an analogous construct for excessive mea- sures seemed to make them much less tractable to a proba- bilistic analysis. This point of view changed radically with the appearance of the pioneering paper by Fitzsimmons and Maisonneuve [FM86] who showed that a certain stationary process associated with an excessive measure could be used to study excessive measures probabilistically. These station- ary processes or measures had been constructed by Kuznetsov [Ku74] extending earlier work of Dynkin. It is now common to call them Kuznetsov measures. Following the Fitzsimmons- Maisonneuve paper there was renewed interest and remarkable progress in the study of excessive measures.
The purpose of this monograph is to organize under one cover and prove under standard hypotheses many of these recent results in the theory of excessive measures. The two basic tools in this recent development are Kuznet- sov measures mentioned above and the energy functional.

1. Notation and Preliminaries.- 2. Excessive Measures.- 3. The Energy Functional.- 4. Balayage of Excessive Measures.- 5. Potential Theory of Excessive Measures.- 6. Kuznetsov Measures.- 7. Kuznetsov Measures II.- 8. Homogeneous Random Measures.- 9. Flows and Palm Measures.- 10. Palm Measures and Capacity.- 11. Exit Systems and Applications.- Appendix A.- Appendix B.- Notation Index.

Erscheint lt. Verlag	1.10.2011
Reihe/Serie	Probability and Its Applications
Zusatzinfo	X, 190 p.
Verlagsort	New York
Sprache	englisch
Maße	152 x 229 mm
Themenwelt	Sachbuch/Ratgeber ► Natur / Technik ► Garten
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	1-4612-8036-2 / 1461280362
ISBN-13	978-1-4612-8036-1 / 9781461280361
Zustand	Neuware