The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 6, Number 3 (1996), 1041-1043.
Sample quantiles of stochastic processes with stationary and independent increments
The purpose of this note is to obtain a representation of the distribution of the $\alpha$-quantile of a process with stationary and independent increments as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for a Brownian motion. The proof is based on already known discrete time results.
Ann. Appl. Probab., Volume 6, Number 3 (1996), 1041-1043.
First available in Project Euclid: 18 October 2002
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Dassios, Angelos. Sample quantiles of stochastic processes with stationary and independent increments. Ann. Appl. Probab. 6 (1996), no. 3, 1041--1043. doi:10.1214/aoap/1034968241. https://projecteuclid.org/euclid.aoap/1034968241