Self-similar solution for fractional Laplacian in cones
Probability
2023-11-09 v2
Abstract
We construct a self-similar solution of the heat equation for the fractional Laplacian with Dirichlet boundary conditions in every fat cone. As applications, we give the Yaglom limit and entrance law for the corresponding killed isotropic stable L\'{e}vy process and precise large-time asymptotics for solutions of the Cauchy problem in the cone.
Keywords
Cite
@article{arxiv.2307.01825,
title = {Self-similar solution for fractional Laplacian in cones},
author = {Krzysztof Bogdan and Piotr Knosalla and Łukasz Leżaj and Dominika Pilarczyk},
journal= {arXiv preprint arXiv:2307.01825},
year = {2023}
}
Comments
We provided some examples to illustrate our findings