A1 Journal article (refereed)
Self-similar solution for fractional Laplacian in cones (2024)

Bogdan, K., Knosalla, P., Leżaj, Ł., & Pilarczyk, D. (2024). Self-similar solution for fractional Laplacian in cones. Electronic Journal of Probability, 29, Article 54. https://doi.org/10.1214/24-EJP1111

JYU authors or editors

Publication details

All authors or editors: Bogdan, Krzysztof; Knosalla, Piotr; Leżaj, Łukasz; Pilarczyk, Dominika

Journal or series: Electronic Journal of Probability

eISSN: 1083-6489

Publication year: 2024

Publication date: 01/01/2024

Volume: 29

Article number: 54

Publisher: Institute of Mathematical Statistics

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1214/24-EJP1111

Publication open access: Openly available

Publication channel open access: Open Access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/94672

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2307.01825v2

Abstract

We construct a self-similar solution of the heat equation for the fractional Laplacian with Dirichlet boundary conditions in every fat cone. Furthermore, we give the entrance law from the vertex and the Yaglom limit for the corresponding killed isotropic stable Lévy process and precise large-time asymptotics for solutions of the Cauchy problem in the cone.

Keywords: stochastic processes; Markov chains

Free keywords: cone; Dirichlet heat kernel; entrance law; Martin kernel; Stable process; Yaglom limit

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2024

Preliminary JUFO rating: 2