Solving BSDE with adaptive control variate. A note on the rate of convergence of the operator P^k

Emmanuel Gobet (1) , Céline Labart (2)

1 MATHFI - Mathématiques financières
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

This note is a complement of the paper "Solving BSDE with adaptive control variate". It deals with the convergence of the approximating operator P, based on a non parametric regression technique called local averaging. Although the computations are quite standard (see Hardle '92, Gyorfi etal. '02), the specificities of the paper are the following: - the support of the variables is unbounded; - the error has to be measured using specific L2-norms; - errors on the gradient are provided.

Domaines: Probabilités [math.PR]; Théorie [stat.TH]

Emmanuel Gobet, Céline Labart. Solving BSDE with adaptive control variate. A note on the rate of convergence of the operator P^k. 2009. ⟨hal-00373349⟩