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Generalized Poisson–Kac Processes: Basic Properties and Implications in Extended Thermodynamics and Transport

  • Massimiliano Giona EMAIL logo , Antonio Brasiello and Silvestro Crescitelli

Abstract

We introduce a new class of stochastic processes in Rn, referred to as generalized Poisson–Kac (GPK) processes, that generalizes the Poisson–Kac telegrapher’s random motion in higher dimensions. These stochastic processes possess finite propagation velocity, almost everywhere smooth trajectories, and converge in the Kac limit to Brownian motion. GPK processes are defined by coupling the selection of a bounded velocity vector from a family of N distinct ones with a Markovian dynamics controlling probabilistically this selection. This model can be used as a probabilistic tool for a stochastically consistent formulation of extended thermodynamic theories far from equilibrium.

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Received: 2015-10-13
Revised: 2015-12-12
Accepted: 2016-1-6
Published Online: 2016-2-10
Published in Print: 2016-4-1

©2016 by De Gruyter Mouton

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