Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation
Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation
In this paper we develop a general approach for investigating the asymptotic distribution of functionals $X_n=f((Z_{n+k})_{k\in \mathbf {Z}})$ of absolutely regular stochastic processes $(Z_n)_{n\in \mathbf {Z}}$. Such functionals occur naturally as orbits of chaotic dynamical systems, and thus our results can be used to study probabilistic aspects of dynamical systems. …