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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
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