An Erdős-Révész type law of the iterated logarithm for order statistics of a stationary Gaussian process (Q1745279)

In this paper, an Erdős-Révéz-type law of the iterated logarithm lower bound on \(\xi_p(t)\) is proved, where \(\xi_p(t):=\sup_{0\leq s\leq t}\{X_{r:n}(s)\geq f_p(s)\}\), \(X_{r:n}\) is the order statistics process with respect to a stationary Gaussian process \(X(t)\), and \(f_p(t)\), \(p>1\), is a family of some functions.