Weak Error for stable driven SDEs: expansion of the densities

Valentin Konakov (1) , Stephane Menozzi (2)

1 CMI RAS - Central economics Mathematical institute
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Consider a multidimensional SDE of the form $X_t = x+\int_{0}^{t} b(X_{s-})ds+\int{0}^{t} f(X_{s-})dZ_s$ where $(Z_s)_{s\ge 0}$ is a symmetric stable process. Under suitable assumptions on the coefficients the unique strong solution of the above equation admits a density w.r.t. the Lebesgue measure and so does its Euler scheme. Using a parametrix approach, we derive an error expansion at order 1 w.r.t. the time step for the difference of these densities.

Mots clés: Symmetric stable processes; parametrix; Euler scheme

Domaines: Probabilités [math.PR]

Valentin Konakov, Stephane Menozzi. Weak Error for stable driven SDEs: expansion of the densities. 2008. ⟨hal-00331845v1⟩