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

Blandine Bérard Bergery (1) , Pierre Vallois (2, 1)

1 IECN - Institut Élie Cartan de Nancy
2 BIGS - Biology, genetics and statistics

We consider the convergence of the approximation schemes related to Itô's integral and quadratic variation, which have been developed in [13]. 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; stochastic Fubini's theorem; first and second order convergence

Domaines: Probabilités [math.PR]

Blandine Bérard Bergery, Pierre Vallois. Convergence at first and second order of some approximations of stochastic integrals. Séminaire de Probabilités, 2011, Séminaire de probabilités XLIII, LN 2006, pp.241-268. ⟨hal-01285530⟩