Joint law of an Ornstein–Uhlenbeck process and its supremum | Zendy

Christophette BlanchetScalliet | Zendy; Diana Dorobantu | Zendy; Laura Gay | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Joint law of an Ornstein–Uhlenbeck process and its supremum

Author(s) -

Christophette BlanchetScalliet,

Diana Dorobantu,

Laura Gay

Publication year - 2020

Publication title -

journal of applied probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.668

H-Index - 59

eISSN - 1475-6072

pISSN - 0021-9002

DOI - 10.1017/jpr.2020.22

Subject(s) - infimum and supremum , ornstein–uhlenbeck process , mathematics , expression (computer science) , parabolic cylinder function , brownian motion , function (biology) , monte carlo method , statistical physics , probability density function , mathematical analysis , law , stochastic process , statistics , parabolic partial differential equation , physics , partial differential equation , evolutionary biology , computer science , political science , biology , programming language

We propose an expression for the joint density / distribution function for the endpoint of an Ornstein-Uhlenbeck process and its supremum. This law is expressed as an expansion involving parabolic cylinder functions. We obtain this law faster than with a Monte Carol's method. Numerical applications illustrate the interest of this result.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research