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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.

4 votes
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Two-side deviations for ergodic sums

Sure. Here is a recipe to construct such systems. Start from a dynamical systems which preserves a non-atomic probability measure and which is ergodic $(Y, \nu, T)$. Given an integrable random variabl …
D. Thomine's user avatar
8 votes
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Irrational rotation - recurrence times

You can recover this result in two steps: a variation on Birkhoff's ergodic theorem yields the Cesàro convergence of the sums; Cesàro convergence implies Abel convergence. First step: $T_\alpha$ p …
D. Thomine's user avatar