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A sample-path approach to Palm probabilities

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Shaler Stidham Jr.
Shaler Stidham Jr.*
Affiliation:
University of North Carolina
*
∗ Postal address: Department of Operations Research, CB 3180, Smith Building, University of North Carolina, Chapel Hill, NC 27599-3180, USA.
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Abstract

Previous papers have established sample-path versions of relations between marginal time-stationary and event-stationary (Palm) state probabilities for a process with an imbedded point process. This paper extends the use of sample-path analysis to provide relations between frequencies for arbitrary (measurable) sets in function space, rather than just marginal (one-dimensional) frequencies. We define sample-path analogues of the time-stationary and event-stationary (Palm) probability measures for a process with an imbedded point process, and then derive sample-path versions of the Palm transformation and inversion formulas.

Keywords

POINT PROCESSTIME-STATIONARY PROBABILITIESEVENT-STATIONARYPROBABILITIESPALM TRANSFORMATION FORMULAPALM INVERSION FORMULA

MSC classification

Secondary: 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 430 - 437
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research partially supported by a grant from Centre International des Étudiants et Stagiares (C.I.E.S.) while the author was on leave at INRIA, Sophia-Antipolis, Valbonne, France (1991–92).

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