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On a conjecture for the non-existence of the expectation of randomly stopped sums

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Claude Lefèvre  and
Sergey Utev
Claude Lefèvre*
Affiliation:
Université Libre de Bruxelles
Sergey Utev*
Affiliation:
Novosibirsk University
*
∗Postal address: Institut de Statistique C.P.210, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Bruxelles, Belgique.
∗∗Postal address: Institute of Mathematics, Universitetsky pr.4, Novosibirsk 90, 630090, Russia.
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Abstract

In a recent paper on the validity of Wald's equation, Roters (1994) raised an important question on the non-existence of the expectation of randomly stopped sums. The purpose of this note is to answer the question in the affirmative. As a consequence, an old question by Taylor (1972) also gets a positive answer.

Keywords

STOPPING TIMEWALD'S EQUATION

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60G50: Sums of independent random variables; random walks
Type
Short Communications
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1138 - 1141
Copyright
Copyright © Applied Probability Trust 1995 

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References

Roters, M. (1994) On the validity of Wald's equation. J Appl. Prob. 31, 949–957.Google Scholar
Taylor, H. M. (1972) Bounds for stopped partial sums. Ann. Math. Statist. 43, 733–747.Google Scholar