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2009•Stochastic Analysis and ApplicationsRequires access

Some Limit Theorems for Linear Processes Generated by Symmetrically Exchangeable Random Variables

Ke-Ang Fu, Zhang Li

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Abstract

For the linear process , where {a i ; i ≥ 0} is an absolutely summable sequence of real numbers, and {ϵ i ; − ∞ <i < ∞} is a doubly infinite sequence of symmetrically exchangeable random variables with zero means and finite variances, some limit theorems, including the central limit theorem, complete convergence and the law of iterated logarithm, are obtained for the partial sums of the linear processes.

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What this paper is about

For the linear process , where {a i ; i ≥ 0} is an absolutely summable sequence of real numbers, and {ϵ i ; − ∞ <i < ∞} is a doubly infinite sequence of symmetrically exchangeable random variables with zero means and finite variances, some limit theorems, including the central limit theorem, complete convergence and the law of iterated logarithm, are obtained for the partial sums of the linear processes.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

For the linear process , where {a i ; i ≥ 0} is an absolutely summable sequence of real numbers, and {ϵ i ; − ∞ <i < ∞} is a doubly infinite sequence of symmetrically exchangeable random variables with zero means and finite variances, some limit theorems, including the central limit theorem, complete convergence and the law of iterated logarithm, are obtained for the partial sums of the linear processes.

Key concepts: Mathematics, Law of the iterated logarithm, Central limit theorem, Sequence (biology), Limit (mathematics), Logarithm, Law of large numbers, Convergence of random variables

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