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On rate conservation for non-stationary processes

Published online by Cambridge University Press:  14 July 2016

Ravi Mazumdar ,
Raghavan Kannurpatti  and
Catherine Rosenberg
Ravi Mazumdar*
Affiliation:
INRS, Université du Québec
Raghavan Kannurpatti*
Affiliation:
INRS, Université du Québec
Catherine Rosenberg*
Affiliation:
Ecole Polytechnique, Montréal
*
∗ Postal address: INRS Télécommunications, Université du Québec, Ile des Soeurs, PQ, Canada H3E 1H6.
∗ Postal address: INRS Télécommunications, Université du Québec, Ile des Soeurs, PQ, Canada H3E 1H6.
∗∗ Postal address: Départment de Génie Electrique, Ecole Polytechnique, Montréal, PQ, Canada H3C 3A7.
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Abstract

This paper extends the rate conservation principle to cadlag processes whose jumps form a non-stationary point process with a time-dependent intensity. It is shown that this is a direct consequence of path integration and the strong law of large numbers for local martingales. When specialized to mean rates a non-stationary version of Miyazawa's result is obtained which is recovered in the stationary case. Some applications of the result are also given.

Keywords

POINT PROCESSESNON-STATIONARITYMARTINGALES
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 762 - 770
Copyright
Copyright © Applied Probability Trust 1991 

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