Three theorems on ρ* random fields

Miller, Curtis

doi:10.1007/bf02214377

Cited by 24 publications

(10 citation statements)

References 7 publications

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“…The definitions of these can be found in Bradley (2007). Other works on mixing include but are not limited to Miller (1994), Miller (1995) Gaposhkin (1991) and the references therein. Bradley (1997) presents a proof that every ψ ′ -mixing Markov chain is ρ * -mixing.…”

Section: Mixing Coefficientsmentioning

confidence: 99%

On dependence structure of copula-based Markov chains

Longla

2014

ESAIM: PS

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Section: Mixing Coefficientsmentioning

confidence: 99%

On dependence structure of copula-based Markov chains

Longla

2014

ESAIM: PS

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“…Let us note that, since 0 [3] and Peligrad and Gut [11] pointed out the importance of condition (1.2) in estimating the moments of partial sums or of maximum of partial sums. Various limit properties under the condition lim ρ * n < 1 were studied by Bradley [2] and Miller [10].…”

Section: Sequence Of Identically Distributed and Negatively Associatementioning

confidence: 99%

ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ^*-MIXING SEQUENCES

Ko¹,

Kim²,

Ryu³

2008

Communications of the Korean Mathematical Society

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Let {Y i ; −∞ < i < ∞} be a doubly infinite sequence of identically distributed and ρ *-mixing random variables with zero means and finite variances and {a i ; −∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of { P n k=1 P ∞ i=−∞ a i+k Y i /n 1/p ; n ≥ 1} under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191-197.] to the ρ *-mixing case.

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“…In 1997, Curtis Miller [2] did work in finding a continuous spectral density function for a random field with continuous index assuming ρ * (n) → 0 (similar to but stronger than r * (n) → 0) and another condition. A definition of the ρ * coefficient can be found in both [7,8]. In 2000, Bradley [4] showed that a discrete-indexed random field has a continuous spectral density function assuming only ζ (n) → 0.…”

Section: Introduction and Definitionsmentioning

confidence: 98%

A continuous spectral density for a random field of continuous-index

Shaw

2009

Journal of Multivariate Analysis

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a b s t r a c tLinear dependence coefficients are defined for random fields of continuous-index, which are modified from those already defined for random fields indexed by an integer lattice. When a selection of these linear dependence conditions are satisfied, the random field will have a continuous spectral density function. Showing this involves the construction of a special class of random fields using a standard Poisson process and the original random field.

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Three theorems on ρ* random fields

Cited by 24 publications

References 7 publications

On dependence structure of copula-based Markov chains

On dependence structure of copula-based Markov chains

ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ^*-MIXING SEQUENCES

A continuous spectral density for a random field of continuous-index

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Three theorems on ρ* random fields

Cited by 24 publications

References 7 publications

On dependence structure of copula-based Markov chains

On dependence structure of copula-based Markov chains

ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ*-MIXING SEQUENCES

A continuous spectral density for a random field of continuous-index

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Product

Resources

About

ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ^*-MIXING SEQUENCES