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We study a stochastic differential equation in the sense of rough path theorydriven by fractional Brownian rough path with Hurst parameter H (1/3 < H <=1/2) under the ellipticity assumption at the starting point. In such a case,the law of the solution at a fixed time has a kernel, i.e., a density functionwith respect to Lebesgue measure. In this paper we prove a short timeoff-diagonal asymptotic expansion of the kernel under mild additionalassumptions. Our main tool is Watanabe's distributional Malliavin calculus.

Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion