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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.

7 votes
1 answer
940 views

Prove an anti-concentration inequality for a martingale

My problem can be described easily: I have a sequence $(X_l)_{l \in \mathbb{N}}$ of r.v. adapted to some filtration $(\mathcal{F}_l)_{l \in \mathbb{N}}$, such that $\left|X_{l+1}-X_l\right|\le R$ a …