A formula of small time expansion for Young SDE driven by fractional Brownian motion

作者：Yamada Toshihiro^*

来源：Statistics & Probability Letters, 2015, 101: 64-72.

DOI：10.1016/j.spl.2015.02.011

• Small time expansion
• SDEs driven by fractional Brownian motions
• Malliavin calculus
• Young integrals

This paper shows an explicit small time expansion formula of expectation of the solution to Young SDEs driven by fractional Brownian motion H > 1/2. The expansion coefficients are obtained by using Malliavin calculus for fractional Brownian motion. Furthermore, we show an analytically tractable expansion formula for the expectation of the solution to a general one-dimensional Young SDE driven by fractional Brownian motion and confirm the validity of our small time expansion through numerical experiments.

• 出版日期2015-6