In this talk, we discuss the method of stationary phase for a rough differential equation (RDE) driven by the scaled Brownian rough path ${\overline{\varepsilon w}}$. In particular, we give the asymptotic expansion for a certain class of oscillatory functional integrals for the law of the solution of the RDE as $\varepsilon \searrow 0$.
Our approach is based on the techniques developed in the study of Laplace type functional integrals with Bismut-Malliavin's integration by parts formula in the sense of rough paths.
This is a continuation of a series of joint work with Yuzuru Inahama.
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