# Trees and asymptotic expansions for fractional stochastic differential equations

A. Neuenkirch; I. Nourdin; A. Rößler; S. Tindel

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

- Volume: 45, Issue: 1, page 157-174
- ISSN: 0246-0203

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topNeuenkirch, A., et al. "Trees and asymptotic expansions for fractional stochastic differential equations." Annales de l'I.H.P. Probabilités et statistiques 45.1 (2009): 157-174. <http://eudml.org/doc/78013>.

@article{Neuenkirch2009,

abstract = {In this article, we consider an n-dimensional stochastic differential equation driven by a fractional brownian motion with Hurst parameter H>1/3. We derive an expansion for E[f(Xt)] in terms of t, where X denotes the solution to the SDE and f:ℝn→ℝ is a regular function. Comparing to F. Baudoin and L. Coutin, Stochastic Process. Appl.117 (2007) 550–574, where the same problem is studied, we provide an improvement in three different directions: we are able to consider equations with drift, we parametrize our expansion with trees, which makes it easier to use, and we obtain a sharp estimate of the remainder for the case H>1/2.},

author = {Neuenkirch, A., Nourdin, I., Rößler, A., Tindel, S.},

journal = {Annales de l'I.H.P. Probabilités et statistiques},

keywords = {fractional brownian motion; stochastic differential equations; trees expansions; fractional Brownian motion},

language = {eng},

number = {1},

pages = {157-174},

publisher = {Gauthier-Villars},

title = {Trees and asymptotic expansions for fractional stochastic differential equations},

url = {http://eudml.org/doc/78013},

volume = {45},

year = {2009},

}

TY - JOUR

AU - Neuenkirch, A.

AU - Nourdin, I.

AU - Rößler, A.

AU - Tindel, S.

TI - Trees and asymptotic expansions for fractional stochastic differential equations

JO - Annales de l'I.H.P. Probabilités et statistiques

PY - 2009

PB - Gauthier-Villars

VL - 45

IS - 1

SP - 157

EP - 174

AB - In this article, we consider an n-dimensional stochastic differential equation driven by a fractional brownian motion with Hurst parameter H>1/3. We derive an expansion for E[f(Xt)] in terms of t, where X denotes the solution to the SDE and f:ℝn→ℝ is a regular function. Comparing to F. Baudoin and L. Coutin, Stochastic Process. Appl.117 (2007) 550–574, where the same problem is studied, we provide an improvement in three different directions: we are able to consider equations with drift, we parametrize our expansion with trees, which makes it easier to use, and we obtain a sharp estimate of the remainder for the case H>1/2.

LA - eng

KW - fractional brownian motion; stochastic differential equations; trees expansions; fractional Brownian motion

UR - http://eudml.org/doc/78013

ER -

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