Almost sure invariance principles for mixing sequences of random variables

Qi Man Shao

Almost sure invariance principles for mixing sequences of random variables

Qi Man Shao^*

^*Corresponding author for this work

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

92 Citations (Scopus)

Abstract

An almost sure invariance principle for stationary mixing sequences of random variables with mean zero and finite variance is obtained when the mixing rate satisfies Σ_nø^{1 2}(2ⁿ) < ∞ or ρ(n)= O(log^-r n) for some r > 1. A similar result is also given under a higher moment condition.

Original language	English
Pages (from-to)	319-334
Number of pages	16
Journal	Stochastic Processes and their Applications
Volume	48
Issue number	2
Publication status	Published - Nov 1993
Externally published	Yes

Keywords

almost sure invariance principle
law of the iterated logarithm
partial sums
ø-mixing
ρ-mixing

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https://hdl.handle.net/1783.1/42717

Cite this

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title = "Almost sure invariance principles for mixing sequences of random variables",

abstract = "An almost sure invariance principle for stationary mixing sequences of random variables with mean zero and finite variance is obtained when the mixing rate satisfies Σn{\o} 1 2(2n) < ∞ or ρ(n)= O(log-r n) for some r > 1. A similar result is also given under a higher moment condition.",

keywords = "almost sure invariance principle, law of the iterated logarithm, partial sums, {\o}-mixing, ρ-mixing",

author = "Shao, \{Qi Man\}",

year = "1993",

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language = "English",

volume = "48",

pages = "319--334",

journal = "Stochastic Processes and their Applications",

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TY - JOUR

T1 - Almost sure invariance principles for mixing sequences of random variables

AU - Shao, Qi Man

PY - 1993/11

Y1 - 1993/11

N2 - An almost sure invariance principle for stationary mixing sequences of random variables with mean zero and finite variance is obtained when the mixing rate satisfies Σnø 1 2(2n) < ∞ or ρ(n)= O(log-r n) for some r > 1. A similar result is also given under a higher moment condition.

AB - An almost sure invariance principle for stationary mixing sequences of random variables with mean zero and finite variance is obtained when the mixing rate satisfies Σnø 1 2(2n) < ∞ or ρ(n)= O(log-r n) for some r > 1. A similar result is also given under a higher moment condition.

KW - almost sure invariance principle

KW - law of the iterated logarithm

KW - partial sums

KW - ø-mixing

KW - ρ-mixing

UR - https://www.scopus.com/pages/publications/38248999802

M3 - Journal Article

SN - 0304-4149

VL - 48

SP - 319

EP - 334

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

Almost sure invariance principles for mixing sequences of random variables

Abstract

Keywords

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