Parametrix method for the first hitting time of an elliptic diffusion with irregular coefficients

On Some Asymptotic Expansions of Skew Diffusions

“…As we want to take limits in (11), we need to prove the uniform integrability of the integrands. We note here that the estimate in (9) can not be directly used here because formula (11) is not valid for y = 0.…”

“…For a review on these subjects, we refer the reader to [12]. It has also recently been revisited in a series of works [1,7,4] to provide some probabilistic representation and integration by parts formula of the marginal law of various processes as an alternative to standard Malliavin calculus techniques or to establish the well-posedness in the weak sense of some degenerate stochastic differential equations (SDEs for short) [8,9].…”