Advanced Search

Suppose that {Xn, n ≥ 0} is a stationary Markov chain and V is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem (CLT) if [...] [...] converge in law to a normal random variable, as N → +∞. For a stationary Markov chain with the L2 spectral gap the theorem holds for all V such that V (X0) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables V for...

Suppose that $\{Xn:n\ge 0\}$ is a stationary Markov chain and $V$ is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem (CLT) if $Y_n:=N^{-1/2}{\sum }_{n=0}^{N}V\left(X_n\right)$ converge in law to a normal random variable, as $N\to +\infty$. For a stationary Markov chain with the $L^2$ spectral gap the theorem holds for all $V$ such that $V\left(X_0\right)$ is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables $V$ for which the CLT holds for a class...