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Simpler conditions for Wald equations

Published online by Cambridge University Press:  14 July 2016

B. M. Brown  and
G. K. Eagleson
B. M. Brown
Affiliation:
Cambridge University
G. K. Eagleson
Affiliation:
Cambridge University
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Abstract

If T is a stopping time on a martingale {St }, the mth order moments of T and ST (for integers m ≧ 2) are related by an identity known as a Wald equation of order m. Wald equations hold under certain conditions, which are simplified in this paper by showing that among the set of previously known conditions, some are implied by the others.

Keywords

MARTINGALESTOPPING TIMEWALD EQUATIONINDEPENDENT STATIONARYINCREMENTS

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 451 - 455
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Brown, B. M. (1969) Moments of a stopping rule related to the central limit theorem. Ann. Math. Statist. 40, 1236–1249.CrossRefGoogle Scholar
[2] Burkholder, D. L. (1966) Martingale transforms. Ann. Math. Statist. 37, 1494–1504.CrossRefGoogle Scholar
[3] Hall, W. J. (1970) On Wald equations in continuous time. J. Appl. Prob. 7, 59–68.CrossRefGoogle Scholar