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Joint Law of an Ornstein-Uhlenbeck Process and its Supremum

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01935756
Contributor : Laura Gay <>
Submitted on : Tuesday, November 27, 2018 - 9:30:42 AM
Last modification on : Monday, February 17, 2020 - 10:03:35 AM
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  • HAL Id : hal-01935756, version 1

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Christophette Blanchet-Scalliet, Diana Dorobantu, Laura Gay. Joint Law of an Ornstein-Uhlenbeck Process and its Supremum. Journal of Applied Probability, Applied Probability Trust, In press, 57 (2). ⟨hal-01935756⟩

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