Stochastic regularization effects of semi-martingales on random functions

Romain Duboscq (1, 2) , Anthony Réveillac (1, 2)

1 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse
2 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper we address an open question formulated in [17]. That is, we extend the Itô-Tanaka trick, which links the time-average of a deterministic function f depending on a stochastic process X and F the solution of the Fokker-Planck equation associated to X, to random mappings f. To this end we provide new results on a class of adpated and non-adapted Fokker-Planck SPDEs and BSPDEs.

Mots clés: (Backward) Stochastic Partial Differential Equations; Malliavin calculus; Stochastic regularization

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

Romain Duboscq, Anthony Réveillac. Stochastic regularization effects of semi-martingales on random functions. Journal de Mathématiques Pures et Appliquées, 2016. ⟨hal-01178614v3⟩