Abstract
McKean (1966), Tanaka (1978), and Sznitman (1984) have obtained existence, uniqueness and asymptotic results for the solution of a Boltzmann type equation, for the cases of Kac’s caricature, Maxwell’s gas and Boltzmann’s gas, respectively. Their methods use Wild’s sums. Here we adapt Tanaka’s method for his asymptotic result to show, with the help of Wild’s sums, the convergence toward the geometric equilibrium of the solution of a Boltzmann type equation related to the Bose-Einstein statistic (r = 1) of quantum mechanics.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Ferland, R., Giroux, G. (1987). The Convergence of the Solution of a Boltzmann Type Equation Related to Quantum Mechanics. In: MacNeill, I.B., Umphrey, G.J., Bellhouse, D.R., Kulperger, R.J. (eds) Advances in the Statistical Sciences: Applied Probability, Stochastic Processes, and Sampling Theory. The University of Western Ontario Series in Philosophy of Science, vol 34. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4786-3_7
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DOI: https://doi.org/10.1007/978-94-009-4786-3_7
Publisher Name: Springer, Dordrecht
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