Boltzmann Processes

In [1] we identify the stochastic process which has, as the corresponding Fokker-Planck equation, the Boltzmann equation. This means that we identify the stochastic process which describes the dynamics in position and velocity of one molecule of a rarefied gas which expands in a vacuum according to the Boltzmann equation. We call this the Boltzmann process. We show that this is the solution of a McKean-Vlasov type stochastic differential equation with Poisson noise. All cases are considered here: hard sphere cut-off case, considered by Boltzmann, as well as soft and hard potentials. In [2] we prove the existence of the solution of this Mc Kean-Vlasov SDE for the hard sphere cut-off case. Bibliografia [1] On the construction and identification of Boltzmann processes, S. Albeverio, B. Rüdiger, P. Sundar, Ensaios Matematicos Vol. 38, 2023. [2] (an improved version of) Identification and existence of Boltzmann processes, B. Rüdiger, P. Sundar arxiv 2301.08662.