On normal approximation of discounted and strongly mixing random variables

Abstract

We estimate the difference |Eh(Z_v)-Eh(N)|for bounded functions h: R->R satisfying the Lipschitz condition, where [...] with discount factor v such that 0<v<1. Here {X_n,n>=0} is a sequence of strongly mixing random variables with EX_n=0, and N is a standard normal random variable. In a particular case, the obtained upper bounds are of order [...].

Gauti |Eh(Z_v)-Eh(N)| įverčiai aprėžtai funkcijai h: R->R (R yra realioji tiesė), tenkinančiai Lipšico sąlygą, kur [...] yra neatsitiktinė konstanta, taip vadinamas nuolaidos daugiklis. Reikalaujama, kad a.d. seka {X_n,n>=0} tenkintų stipraus susimaišymo sąlygą (1).