On Some Asymptotic Expansions of Skew Diffusions

Abstract

Relying on a perturbation technique of Markov semigroup, also known as the parametrix method, we establish some asymptotic expansion for the Markov semigroup generated by a skew diffusion process with respect to a small parameter. Though the approach developed here is general, we focus on the case of short time and small skew heat kernel expansions.