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Relativistic analysis of stochastic kinematics
Massimiliano Giona
The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochas…
Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part III Extensions and applications to kinetic theory and transport
Massimiliano Giona, Antonio Brasiello, Silvestro Crescitelli
This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i)…
Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part II Irreversibility, Norms and Entropies
Massimiliano Giona, Antonio Brasiello, Silvestro Crescitelli
In this second part, we analyze the dissipation properties of Generalized Poisson-Kac (GPK) processes, considering the decay of suitable -norms and the definition of entropy f…
Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part I Basic theory
Massimiliano Giona, Antonio Brasiello, Silvestro Crescitelli
This article introduces the notion of Generalized Poisson-Kac (GPK) processes which generalize the class of "telegrapher's noise dynamics" introduced by Marc Kac in 1974, usingPois…
Markovian nature, completeness, regularity and correlation properties of Generalized Poisson-Kac processes
Massimiliano Giona, Antonio Brasiello, Silvestro Crescitelli
We analyze some basic issues associated with Generalized Poisson-Kac (GPK) stochastic processes, starting from the extended notion of the Markovian condition. The extended Markovia…