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Extended Poisson-Kac theory: A unifying framework for stochastic processes with finite propagation velocity

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FD2W02 - Fractional kinetics, hydrodynamic limits and fractals

We present a theoretical framework for stochastic processes possessing physically realistic finite propagation velocity [1]. Our approach is motivated by the theory of Levy walks, which we embed into an extension of conventional Poisson-Kac processes. The resulting extended theory employs generalised transition rates to model subtle microscopic dynamics, which reproduces non-trivial spatio-temporal correlations on macroscopic scales. It thus enables the modelling of many different kinds of dynamical features, as is illustrated by three examples. [1] M.Giona, A.Cairoli, R.Klages, arXiv:2009.13434 and PRX (2022), in print

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