2019/10/28 by Sigurd Assing, Assing, Sigurd, John R. Herman +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1910.12772
openalex publication_date 2019/10/28 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
It has recently been shown that complete Bernstein functions of the Laplace\noperator map the Dirichlet boundary condition of a related elliptic PDE to the\nNeumann boundary condition. The importance of this mapping consists in being\nable to convert problems involving non-local operators, like fractional\nLaplacians, into ones that only involve differential operators. We generalise\nthis result to diffusion operators associated with stochastic differential\nequations, using a method which is entirely based on stochastic analysis.\n