A Parametrix Approach for some Degenerate Stable Driven SDEs

Lorick Huang (1) , Stephane Menozzi (2, 3)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Higher School of Economics
3 LAP - Laboratoire Analyse et Probabilités

We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak Hörmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the associated generator under some dimension constraints. Also, when the driving noise is scalar and tempered, we establish density bounds reflecting the multi-scale behavior of the process.

Mots clés: Parametrix; Density Estimate; Weak Hörmander; Martingale Problem; Stable driven degenerate SDE

Domaines: Probabilités [math.PR]

Lorick Huang, Stephane Menozzi. A Parametrix Approach for some Degenerate Stable Driven SDEs. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2016, 52 (4), pp.1925-1975. ⟨hal-00947749v2⟩