## The Annals of Applied Probability

### Sample quantiles of stochastic processes with stationary and independent increments

Angelos Dassios

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab., Volume 6, Number 3 (1996), 1041-1043.

Dates
First available in Project Euclid: 18 October 2002

https://projecteuclid.org/euclid.aoap/1034968241

Digital Object Identifier
doi:10.1214/aoap/1034968241

Mathematical Reviews number (MathSciNet)
MR1410129

Zentralblatt MATH identifier
0860.60025

#### Citation

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

#### References

• 1 AKAHORI, J. 1995. Some formulae for a new ty pe of path-dependent option. Ann. Appl. Probab. 5 383 388.