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December, 1976 Une Theorie de la Dualite a Ensemble Polaire Pres II
M. A. Garcia Alvarez
Ann. Probab. 4(6): 947-976 (December, 1976). DOI: 10.1214/aop/1176995939


In 1972, starting from a transient Markov process with a nice semigroup satisfying the absolute continuity hypothesis, P. A. Meyer and I built a nice dual semigroup and then obtained a Martin compactification modulo a polar set. Now, in this paper, we start from this Martin space and study the behavior of the sample paths. We prove that the Martin boundary so constructed appears in the classical form which allows one to describe the final behavior of the sample paths. We also prove that the Martin boundary we construct is an "entrance boundary" such as the Ray boundary. Finally we study a class of additive functionals which ignore the discontinuities of the process in the Martin space and which constitute a nice class of "natural" additive functionals. From all this we conclude that our Martin space is better suited for the study of the process than either the Ray space or the original space.


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M. A. Garcia Alvarez. "Une Theorie de la Dualite a Ensemble Polaire Pres II." Ann. Probab. 4 (6) 947 - 976, December, 1976.


Published: December, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0366.60105
MathSciNet: MR436345
Digital Object Identifier: 10.1214/aop/1176995939

Primary: 60J45
Secondary: 60J50 , 60J55

Keywords: behavior at infinity of the sample paths , co-branching points , conatural additive functionals , entrance boundary , exit boundary , Martin space , reversed process

Rights: Copyright © 1976 Institute of Mathematical Statistics


Vol.4 • No. 6 • December, 1976
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