Approximation schemes associated to a differential equation governed by a Holderian function; the case of fractional Brownian movement.

Approximation schemes associated to a differential equation governed by a Holderian function; the case of fractional Brownian movement. We study here classical approximation schemes (Euler, Milshtein) associated with a differential equation of the type dx(t) = sigma (x(t)) dg(t) + b(x(t)) dt, x(t) is an element of R, where g is a function, supposed Holderian of order a somewhere in (0, 1]. When g = B-H is the trajectory of fractional Brownian movement, we deduce probability properties to refine the results. To cite this article: L Nourdin, C. R. Acad. Sci. Paris, Set. 1340 (2005). (c) 2005 Academie des sciences. Publie par Elsevier SAS. Tous droits reserves.