Abstract

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.

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