Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CENTRAL LIMIT THEOREMS FOR CONDITIONALLY STRONG MIXING AND CONDITIONALLY STRICTLY STATIONARY SEQUENCES OF RANDOM VARIABLES

  • De-Mei Yuan (School of Mathematics and Statistics Chongqing Technology and Business University) ;
  • Xiao-Lin Zeng (School of Mathematics and Statistics Chongqing Technology and Business University)
  • Received : 2023.06.23
  • Accepted : 2024.02.16
  • Published : 2024.07.01
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Abstract

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.

Keywords

Acknowledgement

The authors would like to thank the anonymous referees sincerely for their valuable comments. This work was supported by General Project of Natural Science Foundation of Chongqing (No. CSTB2022NSCQ-MSX1370), the Planning Topics Key Project for 13th Five-Year Plan of Chongqing Education Sciences (No. 2019-GX-118), and the SCR of Chongqing Municipal Education Commission (No. KJZD-M202100801).

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