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This paper presents a novel generic asymptotic expansion formula ofexpectations of multidimensional Wiener functionals through a Malliavincalculus technique. The uniform estimate of the asymptotic expansion is shownunder a weaker condition on the Malliavin covariance matrix of the targetWiener functional. In particular, the method provides a tractable expansion forthe expectation of an irregular functional of the solution to amultidimensional rough differential equation driven by fractional Brownianmotion with Hurst index $H<1/2$, without using complicated fractional integralcalculus for the singular kernel. In a numerical experiment, our expansionshows a much better approximation for a probability distribution function thanits normal approximation, which demonstrates the validity of the proposedmethod.

New asymptotic expansion formula via Malliavin calculus and its application to rough differential equation driven by fractional Brownian motion