Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-29T03:47:40.404Z Has data issue: false hasContentIssue false
  • English
  • Français

A discrete-time proof of Neveu's exchange formula

Part of: Measure-theoretic ergodic theory Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Takis Konstantopoulos  and
Michael Zazanis
Takis Konstantopoulos*
Affiliation:
University of Texas
Michael Zazanis*
Affiliation:
University of Massachusetts
*
∗Postal address: Department of Electrical and Computer Engineering, University of Texas, Austin, TX 78712, USA.
∗∗Postal address: Department of IEOR, University of Massachusetts, Amherst, MA 01003, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Neveu's exchange formula relates the Palm probabilities with respect to two jointly stationary simple point processes. We give a new proof of the exchange formula by using a simple result from discrete time stationary stochastic processes.

Keywords

STATIONARY STOCHASTIC PROCESSESPOINT PROCESSESERGODIC PROCESS

MSC classification

Primary: 60G55: Point processes
Secondary: 60G10: Stationary processes 28D99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 917 - 921
Copyright
Copyright © Applied Probability Trust 1995 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported in part by NSF grant NCR 92–11343.

Research supported in part by NSF grant SES-91–19621.

References

[1] Brémaud, P. (1991) An elementary proof of Sengupta's invariance relation and a remark on Miyazawa's conservation principle. J Appl. Prob. 28, 950–954.CrossRefGoogle Scholar
[2] Brémaud, P. (1993) A Swiss army formula for Palm calculus. J. Appl. Prob. 30, 40–51.CrossRefGoogle Scholar
[3] Franken, P. and Lisek, B. (1982) On Wald's identity for dependent variables. Z. Wahrscheinlichkeitsth. 60, 143–150.CrossRefGoogle Scholar
[4] Franken, P., König, D., Arndt, U. and Schmidt, V. (1981) Queues and Point Processes. Wiley, New York.Google Scholar
[5] Kac, M. (1947) On the notion of recurrence in discrete stochastic processes. Bull. Amer. Math. Soc. 53, 1002–1010.CrossRefGoogle Scholar
[6] Konstantopoulos, T. and Zazanis, M. (1992) Sensitivity analysis for stationary and ergodic queues. Adv. Appl. Prob. 24, 738–750.CrossRefGoogle Scholar
[7] Neveu, J. (1976) Sur les mesures de Palm de deux processus ponctuels stationnaires. Z. Wahrscheinlichkeitsth. 34, 199–203.CrossRefGoogle Scholar
[8] Neveu, J. (1976) Processus ponctuels. In Ecole d'été de Probabilités de St Flour VI. Lecture Notes in Mathematics 598, 249–447. Springer-Verlag, Berlin.Google Scholar