Sample quantiles of heavy tailed stochastic processes (Q1904544)

For a stochastic process \(Y = (Y_t)_{t \in T}\) let the random variable \(Q_\rho (Y)\) denote the sample \(\rho\)-quantile of \(Y\) \((0 \leq \rho < 1)\); i.e. \(Y\) spends at least \(100 \rho\) \% of its ``time'' at or below \(Q_\rho (Y)\) and at least \(100 (1 - \rho)\) \% of its ``time'' at or above \(Q_\rho (Y)\). The authors derive asymptotics for the tail of the sample quantile distribution for the class of infinitely divisible stochastic processes whose Lévy-measures have regularly varying tail.