Joint Law of an Ornstein-Uhlenbeck Process and its Supremum

Christophette Blanchet-Scalliet (1) , Diana Dorobantu (2) , Laura Gay (1)

1 PSPM - Probabilités, statistique, physique mathématique
2 SAF - Laboratoire de Sciences Actuarielle et Financière

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.

Mots clés: Fokker-Planck equation; endpoint; Ornstein-Uhlenbeck process; joint law; supremum

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Christophette Blanchet-Scalliet, Diana Dorobantu, Laura Gay. Joint Law of an Ornstein-Uhlenbeck Process and its Supremum. Journal of Applied Probability, 2020, 57 (2), pp.541-558. ⟨10.1017/jpr.2020.22⟩. ⟨hal-01935756⟩