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ON A GENERALIZATION OF THE STATIONARY EXCESS OPERATOR

Published online by Cambridge University Press:  30 March 2015

Yoav Kerner  and
Andreas Löpker
Yoav Kerner
Affiliation:
Ben-Gurion University of the Negev, P.O.B 653, Beer-Sheva 84105, Israel E-mail: kerneryo@bgu.ac.il
Andreas Löpker
Affiliation:
Helmut Schmidt University Hamburg, 22043 Hamburg, Germany E-mail: lopker@hsu-hh.de
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Abstract

We show that overshoots over Erlang random variables give rise to a natural generalization of the stationary excess operator and its iterates. The new operators can be used to derive expansions for the expectation Eg(X) of a non-negative random variable, similar to Taylor-like expansions encountered when studying stationary excess operators.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 2 , April 2015 , pp. 219 - 232
Copyright
Copyright © Cambridge University Press 2015 

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