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A study for some doubly stochastic model

Title
A study for some doubly stochastic model
Authors
위효정
Issue Date
1997
Department/Major
대학원 통계학과
Keywords
stochastic modelSationary SolutionMarkov ProcessFunctional Central Limit Theorem
Publisher
The Graduate school of Ewha Women's University
Degree
Master
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.
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