Path integral approach to fractional Lévy motion. (English) Zbl 1267.82122
Summary: We give an explicit and simple derivation of the propagator for fractional Lévy motion using path integral methods. Some known forms of propagators, like for Brownian motion, are recovered in limiting cases. We also discuss the associated kinetic equations, as well as some extensions.
MSC:
82C70 | Transport processes in time-dependent statistical mechanics |
81S40 | Path integrals in quantum mechanics |
60J65 | Brownian motion |
60J60 | Diffusion processes |
60G22 | Fractional processes, including fractional Brownian motion |
60G51 | Processes with independent increments; Lévy processes |