27 citations · 95 across the 6 of their papers we have counts for
6 papers
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…
On the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes
Massimiliano Giona, Antonio Brasiello, Silvestro Crescitelli
We analyze the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes, and specifically how they modify the Poissonian switching-time stat…
One-dimensional hyperbolic transport: positivity and admissible boundary conditions derived from the wave formulation
Antonio Brasiello, Silvestro Crescitelli, Massimiliano Giona
We consider the one-dimensional Cattaneo equation for transport of scalar fields such as solute concentration and temperature in mass and heat transport problems, respectively. Alt…