Lévy processes in bounded domains: path-wise reflection scenarios and signatures of confinement. (29th July 2022)

• Record Type: Journal Article
• Authors: Garbaczewski, Piotr; Żaba, Mariusz
• Is Part Of: Journal of physics. Volume 55:Number 30(2022)
• Publication Date: 2022-07-29
• Subjects: path-wise analysis -- reflection scenarios -- random walk approximation -- asymptotic pdfs in the interval -- fractional Laplacian -- reflecting Lévy process -- reflecting boundary data; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac7d1f
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric α -stable Lévy processes, whose permanent residence in a finite interval on a line is secured by a two-sided reflection. Depending on the specific reflection 'mechanism', the inferred jump-type processes differ in their spectral and statistical characteristics, like e.g. relaxation properties, and functional shapes of invariant (equilibrium, or asymptotic near-equilibrium) probability density functions in the interval. The analysis is carried out in conjunction with attempts to give meaning to the notion of a reflecting Lévy process, in terms of the domain of its motion generator, to which an invariant pdf (actually an eigenfunction) does belong.