An Example of a Weak Martingale

Jeremy Berman

doi:10.1214/aop/1176996187

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Home > Journals > Ann. Probab. > Volume 4 > Issue 1 > Article

February, 1976 An Example of a Weak Martingale

Jeremy Berman

Ann. Probab. 4(1): 107-108 (February, 1976). DOI: 10.1214/aop/1176996187

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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.