Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory (Q296530)

Let \((w_t^H)_{t \geq 0}\) be a \(d\)-dimensional fractional Brownian motion with Hurst parameter \(H\in (1/2, 1)\). The author considers the following problem: NEWLINE\[NEWLINE dy_t = \sum_{i=1}^d V_i(y_t) dw_t^{H,i} + V_0(y_t)dt \;\text{ with } y_0 =a \in \mathbb{R}^n .NEWLINE\]NEWLINENEWLINENEWLINEUsing Malliavin calculus and, in particular, Watanabe distribution theory, the author proves a short asymptotic expansion of the density of the solution of this problem in the elliptic case under mild assumptions. This kind of asymptotics was studied in [\textit{F. Baudoin} and \textit{M. Hairer}, Probab. Theory Relat. Fields 139, No. 3--4, 373--395 (2007; Zbl 1123.60038)] and in [\textit{F. Baudoin} and \textit{C. Ouyang}, Stochastic Processes Appl. 121, No. 4, 759--792 (2011; Zbl 1222.60034)] but without using Malliavin calculus.