R.K. Getoor Excessive Measures 9781461280361

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Автор: R.K. Getoor
Название: Excessive Measures
ISBN: 9781461280361
Издательство: Springer
Классификация: ISBN-10: 1461280362
Обложка/Формат: Paperback
Страницы: 190
Вес: 0.28 кг.
Дата издания: 01.10.2011
Серия: Probability and Its Applications
Язык: English
Размер: 229 x 152 x 11
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: The study of the cone of excessive measures associated with a Markov process goes back to Hunts 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.

Excessive Measures, R.K. Getoor