About classical solutions of the path-dependent heat equation

Cristina Di Girolami (1, 2) , Francesco Russo (3, 4)

1 LMM - Laboratoire Manceau de Mathématiques
2 Ud'A - Università degli studi "G. d'Annunzio" Chieti-Pescara [Chieti-Pescara]
3 UMA - Unité de Mathématiques Appliquées
4 OC - Optimisation et commande

This paper investigates two existence theorems for the path-dependent heat equation, which is the Kolmogorov equation related to the window Brownian motion, considered as a C([−T, 0])-valued process. We concentrate on two general existence results of its classical solutions related to different classes of final conditions: the first one is given by a cylindrical non necessarily smooth r.v., the second one is a smooth generic functional.

Mots clés: Window Brownian motion; Path-dependent heat equation; Kolmogorov type equations; Infinite dimensional analysis

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

Cristina Di Girolami, Francesco Russo. About classical solutions of the path-dependent heat equation. Random Operators and Stochastic Equations, 2020, 1, pp.35-62. ⟨10.1515/rose-2020-2028⟩. ⟨hal-01762783v3⟩