In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is amenable to Monte Carlo simulation. We consider the explicit examples of continuous diffusions and jump driven stochastic differential equations with Hölder continuous coefficients.
"A probabilistic interpretation of the parametrix method." Ann. Appl. Probab. 25 (6) 3095 - 3138, December 2015. https://doi.org/10.1214/14-AAP1068