The Annals of Probability

An Example of a Weak Martingale

Jeremy Berman

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Abstract

A sequence of integrable random variables $\{X_n, n \geqq 0\}$ is a weak martingale if $E(X_n \mid X_m) = X_m$ a.s. for all $0 \leqq m < n$. We present an example of a weak martingale which is not a martingale. It is bounded and has countably many paths.

Article information

Source
Ann. Probab. Volume 4, Number 1 (1976), 107-108.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996187

Digital Object Identifier
doi:10.1214/aop/1176996187

Mathematical Reviews number (MathSciNet)
MR391248

Zentralblatt MATH identifier
0344.60032

JSTOR
links.jstor.org

Subjects
Primary: 60G45
Secondary: 60G45

Keywords
Weak martingale martingale example

Citation

Berman, Jeremy. An Example of a Weak Martingale. Ann. Probab. 4 (1976), no. 1, 107--108. doi:10.1214/aop/1176996187. https://projecteuclid.org/euclid.aop/1176996187


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