Limit theorems for some doubly stochastic processes

Oesook Lee

doi:10.1016/s0167-7152(96)00076-4

Limit theorems for some doubly stochastic processes

Oesook Lee

Department of Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider the stochastic processes X_k+1 = Γ_k+1(X_k) + W_k+1 where {Γ_k} is a sequence of nonlinear random functions and {W_k} is a sequence of disturbances. Sufficient conditions for the existence of a unique invariant probability are obtained. Functional central limit theorem is proved for every Lipschitzian function on R.

Original language	English
Pages (from-to)	215-221
Number of pages	7
Journal	Statistics and Probability Letters
Volume	32
Issue number	2
DOIs	https://doi.org/10.1016/s0167-7152(96)00076-4
State	Published - 1 Mar 1997

Keywords

Doubly stochastic process
Functional central limit theorem
Invariant probability
Markov process
Weak convergence

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10.1016/s0167-7152(96)00076-4

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title = "Limit theorems for some doubly stochastic processes",

abstract = "We consider the stochastic processes Xk+1 = Γk+1(Xk) + Wk+1 where \{Γk\} is a sequence of nonlinear random functions and \{Wk\} is a sequence of disturbances. Sufficient conditions for the existence of a unique invariant probability are obtained. Functional central limit theorem is proved for every Lipschitzian function on R.",

keywords = "Doubly stochastic process, Functional central limit theorem, Invariant probability, Markov process, Weak convergence",

author = "Oesook Lee",

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T1 - Limit theorems for some doubly stochastic processes

AU - Lee, Oesook

PY - 1997/3/1

Y1 - 1997/3/1

N2 - We consider the stochastic processes Xk+1 = Γk+1(Xk) + Wk+1 where {Γk} is a sequence of nonlinear random functions and {Wk} is a sequence of disturbances. Sufficient conditions for the existence of a unique invariant probability are obtained. Functional central limit theorem is proved for every Lipschitzian function on R.

AB - We consider the stochastic processes Xk+1 = Γk+1(Xk) + Wk+1 where {Γk} is a sequence of nonlinear random functions and {Wk} is a sequence of disturbances. Sufficient conditions for the existence of a unique invariant probability are obtained. Functional central limit theorem is proved for every Lipschitzian function on R.

KW - Doubly stochastic process

KW - Functional central limit theorem

KW - Invariant probability

KW - Markov process

KW - Weak convergence

UR - https://www.scopus.com/pages/publications/0031091902

U2 - 10.1016/s0167-7152(96)00076-4

DO - 10.1016/s0167-7152(96)00076-4

M3 - Article

AN - SCOPUS:0031091902

SN - 0167-7152

VL - 32

SP - 215

EP - 221

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

Limit theorems for some doubly stochastic processes

Abstract

Keywords

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