Convergence at first and second order of some approximations of stochastic integrals

Blandine Bérard-Bergery (1) , Pierre P. Vallois (1)

1 IECN - Institut Élie Cartan de Nancy

We consider the convergence of the approximation schemes related to Itô's integral and quadratic variation, which have been developed in [8]. First, we prove that the convergence in the a.s. sense exists when the integrand is Hölder continuous and the integrator is a continuous semimartingale. Second, we investigate the second order convergence in the Brownian motion case.

Mots clés: stochastic integration by regularization; quadratic variation; first and second order convergence; stochastic Fubini's theorem

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

Blandine Bérard-Bergery, Pierre P. Vallois. Convergence at first and second order of some approximations of stochastic integrals. Séminaire de Probabilités, 2007, 2006-2011, pp.241-268. ⟨10.1007/978-3-642-15217-7_10⟩. ⟨hal-00292344⟩