Sharp estimates for the convergence of the density of the Euler scheme in small time

Emmanuel Gobet (1) , Celine Labart (2)

1 MATHFI - Mathématiques financières
2 MATHFI - Financial mathematics

In this work, we approximate a diffusion process by its Euler scheme and we study the convergence of the density of the marginal laws. We improve previous estimates especially for small time.

Mots clés: stochastic differential equation; Euler scheme; rate of convergence; Malliavin calculus

Domaines: Probabilités [math.PR]

Emmanuel Gobet, Celine Labart. Sharp estimates for the convergence of the density of the Euler scheme in small time. Electronic Communications in Probability, 2008, 13, pp.352-363. ⟨10.1214/ECP.v13-1393⟩. ⟨hal-00281365⟩