Density Bounds for some Degenerate Stable Driven SDEs

Lorick Huang (1) , Stephane Menozzi (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 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. Also, in the scalar case we establish density bounds reflecting the multi-scale behavior of the process.

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

Domaines: Probabilités [math.PR]

Lorick Huang, Stephane Menozzi. Density Bounds for some Degenerate Stable Driven SDEs. 2014. ⟨hal-00947749v1⟩