CENTRAL LIMIT THEOREMS FOR CONDITIONALLY STRONG MIXING AND CONDITIONALLY STRICTLY STATIONARY SEQUENCES OF RANDOM VARIABLES

From the ordinary notion of upper-tail quantitle function, a new concept called conditionally upper-tail quantitle function given a σ-algebra is proposed. Some basic properties of this terminology and further properties of conditionally strictly stationary sequences are derived. By means of these pr...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 61; no. 4; pp. 713 - 742
Main Authors De-Mei Yuan, Xiao-Lin Zeng
Format Journal Article
LanguageKorean
Published 2024
Subjects
conditional central limit theorem
conditional stationarity
conditionally strong mixing
conditionally uppertail quantile function
Strong mixing
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Summary:From the ordinary notion of upper-tail quantitle function, a new concept called conditionally upper-tail quantitle function given a σ-algebra is proposed. Some basic properties of this terminology and further properties of conditionally strictly stationary sequences are derived. By means of these properties, several conditional central limit theorems for a sequence of conditionally strong mixing and conditionally strictly stationary random variables are established, some of which are the conditional versions corresponding to earlier results under non-conditional case.
Bibliography:KISTI1.1003/JNL.JAKO202420772008124
ISSN:0304-9914