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.
Citation
Jeremy Berman. "An Example of a Weak Martingale." Ann. Probab. 4 (1) 107 - 108, February, 1976. https://doi.org/10.1214/aop/1176996187
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