A study for some doubly stochastic model

Abstract

In this paper, we consider a doubly stochastic process ｛X_(n), n≥0 ｝on R^(k) which is given by X_(n+1)=F_(n)(X_(n))+E_(n), n≥0, where ｛F_(n)｝is a sequence of Lipschitz maps from R^(k) into R^(k) and｛E_(n)｝ is a sequence of random variables on R^(k). Sufficient conditions for the existence of a stationary solution for ｛X_(n)｝, ｛F_(n)；n≥0｝and ｛E_(n)；n≥0｝are sequences of strictly stationary processes, are obtained. Under additional assumption a functional central limit theorem for a Markov process ｛X_(n)｝ on R_(k), where ｛F_(n)；n≥0｝ and ｛E_(n)；n≥0｝are independent and identically distributed processes, is proved for arbitrary Lipschitzian functions on R_(k). ;본 논문에서는 X_(n+1)=F_(n)(X_(n))+E_(n) 의 형태를 갖는 Stochastic Process의 Sationary Solution 이 존재하는 충분조건을 찾고 {X_(n)}가 Markov Process인 상황에서 Functional Central Limit Theorem 를 만족하는 충분조건을 찾는다.