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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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Convergence of conditional expectations in $L_p$ for non-negative adapted processes

Given an adapted processes $(X_n, \mathscr{F}_n)$ that satisfies $X_n \geq 0$ for all $n > 0$ and $\sum\limits_{n=1}^{+\infty} X_n = 1$, can we conclude that $\sum\limits_{n=1}^{+\infty} \mathbb{E}(X_ …
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