A probabilistic interpretation of the parametrix method

Vlad Bally; Arturo Kohatsu-Higa

doi:10.1214/14-aap1068

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arXiv · 1510.06909

A probabilistic interpretation of the parametrix method

Vlad Bally·Arturo Kohatsu-Higa

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Abstract

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.

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Vlad Bally, Arturo Kohatsu-Higa. 2015-10-23. A probabilistic interpretation of the parametrix method. https://doi.org/10.1214/14-aap1068

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