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

Abstract

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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.

How to cite

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Neuenkirch, 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&gt;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&gt;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&gt;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&gt;1/2.
LA - eng
KW - fractional brownian motion; stochastic differential equations; trees expansions; fractional Brownian motion
UR - http://eudml.org/doc/78013
ER -

References

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