A probabilistic interpretation of the parametrix method.
By Vlad Bally, Arturo Kohatsu-Higa. 2015
56 citations recorded by the source corpus.
In this article, we introduce the parametrix method for constructions of fundamental solutions as a general method based on semigroups and difference of generators. This leads to a probabilistic interpretation of the parametrix method that are amenable to Monte Carlo simulation. We consider the explicit examples of continuous diffusions and jump driven stochastic differential equations with Ho lder continuous coefficients.
Subfields: Finance, Numerical Analysis, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/3259760245fea931aeeee455509989befeac3486
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In Finance
In Numerical Analysis
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Citations in the corpus
- On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise (2015, methodology): “screte-time analogue of the parametrix construction for the Eurer scheme for stable-driven SDEs was developed, [CZ13], where two-sided estimates, more precise than those in [Ko89], were obtained, and [BK14], where the probabilistic interpretation of the 8 parametrix construction and its application ”
- Parametrix construction of the transition probability density of the solution to an SDE driven by $\alpha$-stable noise (2014, background): “Let us only mention two recent preprints: [10], where two-sided estimates, more precise than those in [36] are obtained, and [1], where the probabilistic interpretation of the parametrix construction and its application to the Monte-Carlo simulation is developed.”