Borel summation of the small time expansion of some SDE's driven by Gaussian white noise

Abstract

We consider stochastic differential equations driven by Gaussian white noise on ${\mathbb{R}}^d$. % We provide applications to models for financial %markets. Particular attention is given to the kernel $p_t,t\ge 0$ of the transition semigroup associated with the solution process. Under some assumptions on the coefficients, we prove that the small time asymptotic expansion of $p_t$ is Borel summable.

24 pages