Extension Technique for Functions of Diffusion Operators: a stochastic approach
Probability
2021-01-13 v3 Analysis of PDEs
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.
Cite
@article{arxiv.1910.12772,
title = {Extension Technique for Functions of Diffusion Operators: a stochastic approach},
author = {Sigurd Assing and John Herman},
journal= {arXiv preprint arXiv:1910.12772},
year = {2021}
}
Comments
33 pages, corrected two mistakes: added condition (S4) to be satisfied by Krein strings, and added part (b) to Remark 2.13 clarifying the missing contraction property of certain semigroups