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We consider as a random process the distribution of a gas in momentum space as function of the time. The probability of changes of the distribution in infinitesimal time intervals is assumed to be given by the "Stosszahlansatz." For the Rayleigh model of a gas we derive the probability of a distribution as a function of the time. For the Boltzmann gas with microscopic reversibility we show that the probability of a distribution approaches the stationary value in the limit of infinite time.
A. J. F. Siegert (Thu,) studied this question.