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

Sergio Albeverio, Boubaker Smii

Published 2018-10-31Version 1

We consider stochastic differential equations driven by Gaussian white noise on $\R^d$. % We provide applications to models for financial %markets.\\ Particular attention is given to the kernel $p_t,\,t\geq 0$ 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.