Density analysis of BSDEs

Thibaut Mastrolia (1, 2) , Dylan Possamaï (2) , Anthony Réveillac (3, 4)

1 Université Paris Dauphine-PSL
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse
4 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we study the existence of densities (with respect to the Lebesgue measure) for marginal laws of the solution (Y, Z) to a quadratic growth BSDE. Using the (by now) well-established connection between these equations and their associated semi-linear PDEs, together with the Nourdin-Viens formula, we provide estimates on these densities.

Mots clés: BSDEs; Malliavin Calculus; Density analysis; Nourdin-Viens' Formula

Domaines: Probabilités [math.PR]

Thibaut Mastrolia, Dylan Possamaï, Anthony Réveillac. Density analysis of BSDEs. Annals of Probability, 2016, 44 (4), pp.2817 - 2857. ⟨10.1214/15-AOP1035⟩. ⟨hal-01432980⟩