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- W1908376846 abstract "Various forms of the polynomial ergodic theorem (PET) which attracted substantial attention in ergodic theory study the limits of expressions having the form $1/Nsum_{n=1}^NT^{q_1(n)}f_1... T^{q_ell (n)}f_ell$ where $T$ is a weakly mixing measure preserving transformation, $f_i$'s are bounded measurable functions and $q_i$'s are polynomials taking on integer values on the integers. Motivated partially by these results we obtain a central limit theorem for expressions of the form $1/sqrt{N}sum_{n=1}^N (X_1(q_1(n))X_2(q_2(n))... X_ell(q_ell(n))-a_1a_2... a_ell)$ (sum-product limit theorem--SPLIT) where $X_i$'s are fast $alpha$-mixing bounded stationary processes, $a_j=EX_j(0)$ and $q_i$'s are positive functions taking on integer values on integers with some growth conditions which are satisfied, for instance, when $q_i$'s are polynomials of growing degrees. This result can be applied to the case when $X_i(n)=T^nf_i$ where $T$ is a mixing subshift of finite type, a hyperbolic diffeomorphism or an expanding transformation taken with a Gibbs invariant measure, as well, as to the case when $X_i(n)=f_i(xi_n)$ where $xi_n$ is a Markov chain satisfying the Doeblin condition considered as a stationary process with respect to its invariant measure." @default.
- W1908376846 created "2016-06-24" @default.
- W1908376846 creator A5064396762 @default.
- W1908376846 date "2008-09-24" @default.
- W1908376846 modified "2023-09-27" @default.
- W1908376846 title "From Pet to Split" @default.
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