The Annals of Probability

The Expected Value of an Everywhere Stopped Martingale

S. Ramakrishnan and W. D. Sudderth

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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].

Article information

Source
Ann. Probab., Volume 14, Number 3 (1986), 1075-1079.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992461

Digital Object Identifier
doi:10.1214/aop/1176992461

Mathematical Reviews number (MathSciNet)
MR841607

Zentralblatt MATH identifier
0603.60039

JSTOR
links.jstor.org

Subjects
Primary: 60G44: Martingales with continuous parameter
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G42: Martingales with discrete parameter

Keywords
Martingale optional sampling stop rule induction

Citation

Ramakrishnan, S.; Sudderth, W. D. The Expected Value of an Everywhere Stopped Martingale. Ann. Probab. 14 (1986), no. 3, 1075--1079. doi:10.1214/aop/1176992461. https://projecteuclid.org/euclid.aop/1176992461


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