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This third part extends the theory of Generalized Poisson-Kac (GPK) processesto nonlinear stochastic models and to a continuum of states. Nonlinearity istreated in two ways: (i) as a dependence of the parameters (intensity of thestochastic velocity, transition rates) of the stochastic perturbation on thestate variable, similarly to the case of nonlinear Langevin equations, and (ii)as the dependence of the stochastic microdynamic equations of motion on thestatistical description of the process itself (nonlinear Fokker-Planck-Kacmodels). Several numerical and physical examples illustrate the theory.Gathering nonlinearity and a continuum of states, GPK theory provides astochastic derivation of the nonlinear Boltzmann equation, furnishing apositive answer to the Kac's program in kinetic theory. The transition fromstochastic microdynamics to transport theory within the framework of the GPKparadigm is also addressed.

journal of physics. a, mathematical and theoretical

Stochastic foundations of undulatory transport phenomena: Generalized  Poisson-Kac processes - Part III Extensions and applications to kinetic  theory and transport