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Excessive measures. (English) Zbl 0982.31500

Basel: Birkhäuser. viii, 189 p. (1990).
Publisher’s description: This book presents a unified treatment of developments in the potential theory of excessive measures. Included are the various Riesz-type decompositions of an excessive measure, the solidity of the cone of potentials in the natural order, and Fitzsimmons’s representation of one excessive measure in terms of another. Special emphasis is on the use of the energy functional and Kuznetsov measures in the study of excessive measures. Applications are made to the study of capacity, Revuz measures, and Palm measures. An introduction to flows is also included. A special feature is a comprehensive treatment in an appendix of Meyer’s perfection theorem for multiplicative functionals.
The reader may also consult the book by C. Dellacherie and P.-A. Meyer [Probabilités et potential, Chap. 5 (1980; Zbl 0464.60001)] as well as R. K. Getoor and J. Glover’s article [Math. Z. 184, 287-300 (1983; Zbl 0517.60081)].
This monograph provides a valuable resource for researchers and graduate students investigating Markov processes, probability theory, and potential theory.

MSC:

31D05 Axiomatic potential theory
60J45 Probabilistic potential theory
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
31-02 Research exposition (monographs, survey articles) pertaining to potential theory
31C15 Potentials and capacities on other spaces
60J40 Right processes
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