title: Stochastic models for relativistic diffusion.
abstract: The diffusion equation is related to the Schrödinger equation by analytic continuation. The formula E2=p2c2 + m2c4 leads to a relativistic Schrödinger equation, and analytic continuation yields a relativistic diffusion equation that involves fractional calculus. This paper develops stochastic models for relativistic diffusion and equivalent differential equations with no fractional derivatives. Connections to anomalous diffusion are also discussed, along with alternative models.
authors.affiliation: Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand. bbaeumer@maths.otago.ac.nz
authors.forename: Boris
authors.initials: B
authors.lastname: Baeumer
authors.forename: Mark M
authors.initials: MM
authors.lastname: Meerschaert
authors.forename: Mark
authors.initials: M
authors.lastname: Naber