6533b852fe1ef96bd12ab78a
RESEARCH PRODUCT
Lévy processes in bounded domains: path-wise reflection scenarios and signatures of confinement
Mariusz ŻAbaPiotr Garbaczewskisubject
Statistics and Probabilityreflection scenariosasymptotic pdfs in the intervalpath-wise analysisreflecting boundary dataStatistical Mechanics (cond-mat.stat-mech)Probability (math.PR)General Physics and AstronomyFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)reflecting L´evy processMathematics - Analysis of PDEsModeling and SimulationFOS: Mathematicsfractional LaplacianCondensed Matter - Statistical MechanicsMathematics - ProbabilityMathematical Physicsrandom walk approximationAnalysis of PDEs (math.AP)description
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy 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 L\'{e}vy process, in terms of the domain of its motion generator, to which an invariant pdf (actually an eigenfunction) does belong.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-01-01 | Journal of Physics A-Mathematical and Theoretical |