Weighted power variations of fractional Brownian motion B are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by B. The limit of the error between the exact solution and the considered scheme is computed explicitly.
Publié le : 2009-11-15
Classification:
Fractional Brownian motion,
Weighted power variations,
Stochastic differential equation,
Milstein’s type scheme,
Exact rate of convergence,
60F15,
60G15,
60H05,
60H35
@article{1257529893,
author = {Gradinaru, Mihai and Nourdin, Ivan},
title = {Milstein's type schemes for fractional SDEs},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 1085-1098},
language = {en},
url = {http://dml.mathdoc.fr/item/1257529893}
}
Gradinaru, Mihai; Nourdin, Ivan. Milstein’s type schemes for fractional SDEs. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 1085-1098. http://gdmltest.u-ga.fr/item/1257529893/