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INEQUALITIES BETWEEN EVENT AND TIME AVERAGES

Published online by Cambridge University Press:  01 July 1999

J. George Shanthikumar
Affiliation:
Department of IEOR and, Walter A. Haas School of Business, University of California, Berkeley, California 94720
Michael A. Zazanis
Affiliation:
Department of IEOR, University of Massachusetts, Amherst, Massachusetts 01003

Abstract

We consider a stochastic process with an embedded point process in a stationary and ergodic context. Under a “lack of anticipation” assumption for the evolution of the process vis-à-vis the point process, a new better (worse) than used expectation property for the point process, and a monotonicity assumption for the behavior of the process between points, inequalities between event and time averages are obtained. Sample path monotonicity between points is not required (as is the case with existing approaches) and can be replaced with a simple monotonicity requirement for the expected value of the process between points. Inequalities between conditional event and time averages are also examined via a novel argument involving a conditional version of the Palm inversion formula.

Type
Research Article
Copyright
© 1999 Cambridge University Press

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