Trees and asymptotic expansions for fractional stochastic differential equations

keywords: Hull & White model, functional quantization, vector quantization, Karhunen-Loève, Gaussian process, fractional Brownian motion, multifractional Brownian motion,

Keywords: Fractional and multifractional Brownian motions, Gaussian processes, convergence in law, white noise theory, Wick-Itô integral, Skorohod integral, pathwise integral..

First we establish a general result on the regularity with respect to the driven function for the solution of deterministic equations, using the techniques of fractional

We show that the unique solution to a semilinear stochastic differ- ential equation with almost periodic coefficients driven by a fractional Brown- ian motion is almost periodic in

II. The decomposition space U is then the space generated by the translated versions of the scaling function.. The parameter r, hereafter called order, is the number of

In this paper we investigate the accurate convergence of some approximations of m-order integrals which appear when one performs stochastic calculus with respect to processes which

In section 4, we recall some facts on the Malliavin calculus for fractional Brownian motion and some properties of stochastic differential equations driven by a fractional

En s’inspirant de Hairer [ 36 ], Fontbona-Panloup [ 26 ] et Deya-Panloup-Tindel [ 22 ] dans un cadre continu et sous de bonnes hypothèses sur F et sur le bruit gaussien, nous