## The Annals of Probability

### The Expected Value of an Everywhere Stopped Martingale

#### 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

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