Almost sure asymptotic properties of central order statistics from stationary processes

Abstract

In this article, we formulate and prove new properties of conditional quantiles given one of the particular sigma-fields. Next, we use them to investigate almost sure asymptotic behavior of central order statistics which arise from strictly stationary processes. Specifically, we provide a new version of a strong ergodic theorem for central order statistics.

Keywords:

• Central order statistics
• stationary processes
• ergodic processes
• conditional quantiles
• almost sure convergence

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by Warsaw University of Technology (Politechnika Warszawska) under grant no. [504/03934/1120].