New Asymptotic Expansion Formula via Malliavin Calculus and Its Application to Rough Differential Equation Driven by Fractional

Akihiko Takahashi and Toshihiro Yamada
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Akihiko Takahashi: Faculty of Economics, The University of Tokyo
Toshihiro Yamada: Graduate School of Economics, Hitotsubashi University

No CIRJE-F-1215, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper presents a novel generic asymptotic expansion formula of expectations of multidimensional Wiener functionals through a Malliavin calculus technique. The uniform estimate of　the asymptotic expansion is shown under a weaker condition on the Malliavin covariance matrix of the target Wiener functional. In particular, the method provides a tractable expansion for the expectation of an irregular functional of the solution to a multidimensional rough differential equation driven by fractional Brownian motion with Hurst index H

Pages: 20 pages
Date: 2023-06
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2023cf1215

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