Approximation at first and second order of -order integrals of the fractional Brownian motion and of certain semimartingales.
Weighted power variations of iterated Brownian motion.
Dynamical properties and characterization of gradient drift diffusions.
Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion.
Density formula and concentration inequalities with Malliavin calculus.
Delay equations driven by rough paths.
Milstein’s type schemes for fractional SDEs
Weighted power variations of fractional brownian motion are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by . The limit of the error between the exact solution and the considered scheme is computed explicitly.
Multivariate normal approximation using Stein’s method and Malliavin calculus
We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of gaussian fields. Among several examples, we provide an application to a functional version of the Breuer–Major CLT for fields subordinated to a fractional brownian motion.
Central and non-central limit theorems for weighted power variations of fractional brownian motion
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order ≥2 of the fractional brownian motion with Hurst parameter ∈(0, 1), where is an integer. The central limit holds for 1/2<≤1−1/2, the limit being a conditionally gaussian distribution. If <1/2 we show the convergence in 2 to a limit which only depends on the fractional brownian motion, and if >1−1/2 we show the convergence in 2 to a stochastic integral with...
m-order integrals and generalized Itô's formula ; the case of a fractional brownian motion with any Hurst index
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