Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T20:22:52.724Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

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.)

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