2015/10/23 by Vlad Bally, Arturo Kohatsu-Higa · 1 citation
Mathematics · #math.PR
paper · pdf · doi:10.1214/14-aap1068
published as Annals of Applied Probability 2015, Vol. 25, No. 6, 3095-3138 · Published at http://dx.doi.org/10.1214/14-AAP1068 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2015/10/23 · arxiv updated 2015/10/26
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.