Milstein’s type schemes for fractional SDEs

Mihai Gradinaru; Ivan Nourdin

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 4, page 1085-1098
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Gradinaru, Mihai, and Nourdin, Ivan. "Milstein’s type schemes for fractional SDEs." Annales de l'I.H.P. Probabilités et statistiques 45.4 (2009): 1085-1098. <http://eudml.org/doc/78054>.

@article{Gradinaru2009,
abstract = {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.},
author = {Gradinaru, Mihai, Nourdin, Ivan},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {fractional brownian motion; weighted power variations; stochastic differential equation; Milstein’s type scheme; exact rate of convergence; fractional Brownian motion; Milstein's type scheme},
language = {eng},
number = {4},
pages = {1085-1098},
publisher = {Gauthier-Villars},
title = {Milstein’s type schemes for fractional SDEs},
url = {http://eudml.org/doc/78054},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Gradinaru, Mihai
AU - Nourdin, Ivan
TI - Milstein’s type schemes for fractional SDEs
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 4
SP - 1085
EP - 1098
AB - 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.
LA - eng
KW - fractional brownian motion; weighted power variations; stochastic differential equation; Milstein’s type scheme; exact rate of convergence; fractional Brownian motion; Milstein's type scheme
UR - http://eudml.org/doc/78054
ER -

References

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