Fractional Laplacians and L\'{e}vy Flights in Bounded Domains
Piotr Garbaczewski · Acta Physica Polonica B · 2018
We address Lévy-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 Lévy flights, in particular those with an infinite life-time.The related concept of quasi-stationary distributions is briefly mentioned. I. MOTIVATION