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October, 1981 Splitting at Backward Times in Regenerative Sets
Olav Kallenberg
Ann. Probab. 9(5): 781-799 (October, 1981). DOI: 10.1214/aop/1176994308

Abstract

By a backward time is meant a random time which only depends on the future, in the same sense as a stopping time only depends on the past. We show that backward times taking values in a regenerative set $M$ split $M$ into conditionally independent subsets. The conditional distributions of the past may further be identified with the Palm distributions $P_t$ with respect to the local time random measure $\xi$ of $M$ both a.e. $E\xi$ and wherever $\{P_t\}$ has a continuous version. Continuity of $\{P_t\}$ occurs essentially where $E\xi$ has a continuous density, and the latter continuity set may be described rather precisely in terms of the growth rate and regularity properties of the Levy measure of $M$.

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Olav Kallenberg. "Splitting at Backward Times in Regenerative Sets." Ann. Probab. 9 (5) 781 - 799, October, 1981. https://doi.org/10.1214/aop/1176994308

Information

Published: October, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0526.60061
MathSciNet: MR628873
Digital Object Identifier: 10.1214/aop/1176994308

Subjects:
Primary: 60J25
Secondary: 60G57 , 60J55 , 60K05

Keywords: Conditional independence , Local time , Palm distribution , Regenerative set , renewal density

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 5 • October, 1981
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