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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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The $\sigma > 0$ condition in the Central Limit Theorem
In the version of central limit theorem for strictly stationary but weakly dependent (for instance $\alpha$-mixing with fast decaying mixing coefficient) random variables $X_1, X_2, \cdots$, the theor …