Author : R.K. Getoor
Publisher : Birkhäuser
ISBN 13 : 9781461280361
Total Pages : 190 pages
Book Rating : 4.2/5 (83 download)
Book Synopsis Excessive Measures by : R.K. Getoor
Download or read book Excessive Measures written by R.K. Getoor and published by Birkhäuser. This book was released on 2011-10-01 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.