Trees and asymptotic expansions for fractional stochastic differential equations

A. Neuenkirch*, I. Nourdin, A. Rößler, S. Tindel

*Corresponding author for this work
14 Citations (Scopus)


In this article, we consider an n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameterH >1/3. We derive an expansion for E[f (X t )] in terms of t, where X denotes the solution to the SDE and f :ℝ n → 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.

Original languageEnglish
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number1
Pages (from-to)157-174
Number of pages18
Publication statusPublished - 01.02.2009


Dive into the research topics of 'Trees and asymptotic expansions for fractional stochastic differential equations'. Together they form a unique fingerprint.

Cite this