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Documents  37A40 | enregistrements trouvés : 2

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​Assume that a renormalized Birkhoff sum $S_n f/B_n$ converges in distribution to a nontrivial limit. What can one say about the sequence $B_n$? Most natural statements in the literature involve sequences $B_n$ of the form $B_n = n^\alpha L(n)$, where $L$ is slowly varying. We will discuss the possible growth rate of $B_n$ both in the probability preserving case and the conservative case. In particular, we will describe examples where $B_n$ grows superpolynomially, or where $B_{n+1}/B_n$ does not tend to $1$.
​Assume that a renormalized Birkhoff sum $S_n f/B_n$ converges in distribution to a nontrivial limit. What can one say about the sequence $B_n$? Most natural statements in the literature involve sequences $B_n$ of the form $B_n = n^\alpha L(n)$, where $L$ is slowly varying. We will discuss the possible growth rate of $B_n$ both in the probability preserving case and the conservative case. In particular, we will describe examples where $B_n$ ...

37A40 ; 60F05

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We obtain results on mixing and rates of mixing for infinite measure semiflows and flows. The results on rates of mixing rely on operator renewal theory and a Dolgopyat-type estimate. The results on mixing hold more generally and are based on a deterministic (ie non iid) version of Erickson's continuous time strong renewal theorem.

37A25 ; 37A40 ; 37A50 ; 37D25

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