Milstein's type schemes for fractional SDEs
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 4, pp. 1085-1098.

On étudie la vitesse exacte de convergence de certains schémas d'approximation associés à des équations différentielles stochastiques scalaires dirigées par le mouvement brownien fractionnaire B. On utilise le comportement asymptotique des variations à poids de B, et la limite de l'erreur entre la solution et son approximation est calculée de façon explicite.

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.

DOI : 10.1214/08-AIHP196
Classification : 60F15, 60G15, 60H05, 60H35
Mots-clés : fractional brownian motion, weighted power variations, stochastic differential equation, Milstein's type scheme, exact rate of convergence 
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     title = {Milstein's type schemes for fractional {SDEs}},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1085--1098},
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Gradinaru, Mihai; Nourdin, Ivan. Milstein's type schemes for fractional SDEs. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 4, pp. 1085-1098. doi : 10.1214/08-AIHP196. http://www.numdam.org/articles/10.1214/08-AIHP196/

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