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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.
8
votes
Accepted
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 …
4
votes
Accepted
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 …