## Bernoulli

• Bernoulli
• Volume 14, Number 3 (2008), 822-837.

### Asymptotic expansions at any time for scalar fractional SDEs with Hurst index $H>1/2$

#### Abstract

We study the asymptotic expansions with respect to $h$ of $$\mathrm{E}[Δ_hf(X_t)], \mathrm{E}[Δ_hf(X_t)|ℱ_t^X] \mathrm{and} \mathrm{E}[Δ_hf(X_t)|X_t],$$ where $Δ_hf(X_t)=f(X_{t+h})−f(X_t)$, when $f:ℝ→ℝ$ is a smooth real function, $t≥0$ is a fixed time, $X$ is the solution of a one-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst index $H>1/2$ and $ℱ^X$ is its natural filtration.

#### Article information

Source
Bernoulli, Volume 14, Number 3 (2008), 822-837.

Dates
First available in Project Euclid: 25 August 2008

https://projecteuclid.org/euclid.bj/1219669631

Digital Object Identifier
doi:10.3150/08-BEJ124

Mathematical Reviews number (MathSciNet)
MR2537813

Zentralblatt MATH identifier
1158.60025

#### Citation

Darses, Sébastien; Nourdin, Ivan. Asymptotic expansions at any time for scalar fractional SDEs with Hurst index $H&gt;1/2$. Bernoulli 14 (2008), no. 3, 822--837. doi:10.3150/08-BEJ124. https://projecteuclid.org/euclid.bj/1219669631

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