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December 2015 A probabilistic interpretation of the parametrix method
Vlad Bally, Arturo Kohatsu-Higa
Ann. Appl. Probab. 25(6): 3095-3138 (December 2015). DOI: 10.1214/14-AAP1068

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. "A probabilistic interpretation of the parametrix method." Ann. Appl. Probab. 25 (6) 3095 - 3138, December 2015. https://doi.org/10.1214/14-AAP1068

Information

Received: 1 June 2013; Revised: 1 June 2014; Published: December 2015
First available in Project Euclid: 1 October 2015

zbMATH: 1329.35164
MathSciNet: MR3404632
Digital Object Identifier: 10.1214/14-AAP1068

Subjects:
Primary: 35K10, 35K15, 65C20
Secondary: 65C05, 65C30

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 6 • December 2015
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