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Results tagged with limits-and-convergence
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user 12978
Convergence of series, sequences and functions and different modes of convergence.
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Is there a way to find $\limsup$ and $\liminf$ for ergodic processes almost surely?
For ergodic $X_n$, almost surely
$$\limsup_n f(X_n) = \sup_n f(X_n) = \sup \{a \in \mathbb{R} : Pr(f(X_0) > a) > 0\}.$$
In other words, by recurrence, what can happen (with positive probability) wil …
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