Journal of the
Korean Mathematical Society JKMS

From the ordinary notion of upper-tail quantitle function, a new concept called conditionally upper-tail quantitle function given a $\sigma$-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: Strong mixing, conditionally strong mixing, conditionally upper-tail quantile function, conditional stationarity, conditional central limit theorem

MSC numbers: 60E10, 60E15, 60G10

Supported by: 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).