Joint law of an Ornstein–Uhlenbeck process and its supremum-Reference-Cited by-同舟云学术

Joint law of an Ornstein–Uhlenbeck process and its supremum

Published:2020-06 Issue:2 Volume:57 Page:541-558
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:J. Appl. Probab.

Author:

Blanchet-Scalliet Christophette,Dorobantu Diana,Gay Laura

Abstract

AbstractLet X be an Ornstein–Uhlenbeck process driven by a Brownian motion. We propose an expression for the joint density / distribution function of the process and its running supremum. This law is expressed as an expansion involving parabolic cylinder functions. Numerically, we obtain this law faster with our expression than with a Monte Carlo method. Numerical applications illustrate the interest of this result.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

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