Total variation convergence for numerical schemes for diffusions with irregular coefficients: An application to the CIR process

Clément Rey (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this paper, we propose a method to prove the total variation convergence for numerical schemes for Stochastic Dierential Equation (SDE) with irregular coecient. In particular, we will consider SDE with locally smooth coecients. In a rst part, we present this method and in a second time, we apply it to the CIR process. We will consider the weak second order scheme introduced in [2] and we will prove that this scheme also converges towards the diusion for the total variation distance. This convergence will take place with almost order two.

Domaines: Probabilités [math.PR]

Clément Rey. Total variation convergence for numerical schemes for diffusions with irregular coefficients: An application to the CIR process. 2016. ⟨hal-01412024v1⟩