A PROBABILISTIC INTERPRETATION OF THE PARAMETRIX METHOD

• 成果类型: Article
• 署名作者: Bally, Vlad; Kohatsu-Higa, Arturo
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Inria; Ritsumeikan University; Japan Science & Technology Agency (JST)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1068
• 发表日期: 2015
• 页码: 3095-3138
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; local limit-theorems; transition densities; DIFFUSIONS; expansion; error

摘要

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 Holder continuous coefficients.