Extension Technique for Functions of Diffusion Operators: a stochastic approach

Sigurd Assing; John Herman

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arXiv · 1910.12772

Extension Technique for Functions of Diffusion Operators: a stochastic approach

Sigurd Assing·John Herman

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Abstract

It has recently been shown that complete Bernstein functions of the Laplace operator map the Dirichlet boundary condition of a related elliptic PDE to the Neumann boundary condition. The importance of this mapping consists in being able to convert problems involving non-local operators, like fractional Laplacians, into ones that only involve differential operators. We generalise this result to diffusion operators associated with stochastic differential equations, using a method which is entirely based on stochastic analysis.

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Sigurd Assing, John Herman. 2019-10-28. Extension Technique for Functions of Diffusion Operators: a stochastic approach. https://arxiv.org/abs/1910.12772

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