A Small Noise Asymptotic Expansion for Young SDE Driven by Fractional Brownian Motion: A Sharp Error Estimate With Malliavin Calculus |
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Authors: | Toshihiro Yamada |
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Affiliation: | Graduate School of Economics, Hitotsubashi University, Tokyo, Japan, and Graduate School of Economics, University of Tokyo, Tokyo, Japan |
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Abstract: | This article shows an analytically tractable small noise asymptotic expansion with a sharp error estimate for the expectation of the solution to Young’s pathwise stochastic differential equations (SDEs) driven by fractional Brownian motions with the Hurst index H > 1/2. In particular, our asymptotic expansion can be regarded as small noise and small time asymptotics by the error estimate with Malliavin culculus. As an application, we give an expansion formula in one-dimensional general Young SDE driven by fractional Brownian motion. We show the validity of the expansion through numerical experiments. |
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Keywords: | Asymptotic expansion SDEs driven by fractional Brownian motions Young integrals Malliavin calculus |
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