Riassunto analitico
This thesis deals with some probabilistic representations for solutions to various Boltzmann-like equations. The pioneer in this kind of research was H.P McKean, who discovered the first representations in 1966-1967.
Due to recent, successful revisitation and application of McKean's results - which has led to the soluion to some important, unproved conjectures in the realm of kinetic theory - the thesis contains a brief review of these recent achievements, and is aimed at extending the probabilistic representation also to Boltzmann-like equations with non-Maxwellian collision kernels.
This is a first attempt to initiate a new line of research, to be developed in successive works.
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Abstract
This thesis deals with some probabilistic representations for solutions to various Boltzmann-like equations. The pioneer in this kind of research was H.P McKean, who discovered the first representations in 1966-1967.
Due to recent, successful revisitation and application of McKean's results - which has led to the soluion to some important, unproved conjectures in the realm of kinetic theory - the thesis contains a brief review of these recent achievements, and is aimed at extending the probabilistic representation also to Boltzmann-like equations with non-Maxwellian collision kernels.
This is a first attempt to initiate a new line of research, to be developed in successive works.
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