6533b826fe1ef96bd1284721

RESEARCH PRODUCT

Fractional Laplacians and Levy flights in bounded domains

Piotr Garbaczewski

subject

Mathematics - Spectral TheoryMathematics - Analysis of PDEsStatistical Mechanics (cond-mat.stat-mech)FOS: MathematicsFOS: Physical sciencesMathematical Physics (math-ph)Mathematics::Spectral TheorySpectral Theory (math.SP)Condensed Matter - Statistical MechanicsMathematical PhysicsAnalysis of PDEs (math.AP)

description

We address L\'{e}vy-stable stochastic processes in bounded domains, with a focus on a discrimination between inequivalent proposals for what a boundary data-respecting fractional Laplacian (and thence the induced random process) should actually be. Versions considered are: restricted Dirichlet, spectral Dirichlet and regional (censored) fractional Laplacians. The affiliated random processes comprise: killed, reflected and conditioned L\'{e}vy flights, in particular those with an infinite life-time. The related concept of quasi-stationary distributions is briefly mentioned.

yearjournalcountryeditionlanguage
2018-02-27
https://dx.doi.org/10.48550/arxiv.1802.09853