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July, 1986 The Expected Value of an Everywhere Stopped Martingale
S. Ramakrishnan, W. D. Sudderth
Ann. Probab. 14(3): 1075-1079 (July, 1986). DOI: 10.1214/aop/1176992461

Abstract

If the coordinate random variables $\{X_t\}$ on either $C\lbrack 0, \infty)$ or $D\lbrack 0, \infty)$ form a martingale, then for every stopping time $\tau$ which is everywhere finite, $E(X_\tau)$, if defined, equals $E(X_0)$. This version of the optional sampling theorem is not covered by Doob's classical result [1].

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S. Ramakrishnan. W. D. Sudderth. "The Expected Value of an Everywhere Stopped Martingale." Ann. Probab. 14 (3) 1075 - 1079, July, 1986. https://doi.org/10.1214/aop/1176992461

Information

Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0603.60039
MathSciNet: MR841607
Digital Object Identifier: 10.1214/aop/1176992461

Subjects:
Primary: 60G44
Secondary: 60G40 , 60G42

Keywords: martingale , optional sampling , stop rule induction

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 3 • July, 1986
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