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

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.

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.

DOI : https://doi.org/10.1214/08-AIHP196
Classification:  60F15,  60G15,  60H05,  60H35
Keywords: fractional brownian motion, weighted power variations, stochastic differential equation, Milstein's type scheme, exact rate of convergence
@article{AIHPB_2009__45_4_1085_0,
     author = {Gradinaru, Mihai and Nourdin, Ivan},
     title = {Milstein's type schemes for fractional SDEs},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {45},
     number = {4},
     year = {2009},
     pages = {1085-1098},
     doi = {10.1214/08-AIHP196},
     zbl = {1197.60070},
     mrnumber = {2572165},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2009__45_4_1085_0}
}
Gradinaru, Mihai; Nourdin, Ivan. Milstein's type schemes for fractional SDEs. Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 4, pp. 1085-1098. doi : 10.1214/08-AIHP196. http://www.numdam.org/item/AIHPB_2009__45_4_1085_0/

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