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An inequality for a metric in a random collision process

Published online by Cambridge University Press:  14 July 2016

Shōichi Nishimura
Shōichi Nishimura*
Affiliation:
Tokyo Institute of Technology
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Abstract

A random collision process with transition probabilities belonging to the same type of distribution is considered. It was proved that if the characteristic function of the initial distribution has a positive radius of convergence, then the sequence {Fn (x)} converges weakly to a distribution G(x) [9]. We define a metric e 1[Fn ;G], which is analogous to the functional e[f] introduced by Tanaka to Kac's model of Maxwellian gas [10]. We prove that e 1[Fn ; G] is monotone non-increasing as n → ∞, and also the convergence of the sequence {Fn (x)} under the weaker assumption that for some a > 1 the initial distribution has an ath moment.

Keywords

RANDOM COLLISION PROCESSKAC'S MODEL OF A MAXWELLIAN GASFUNCTIONAL eGLOBAL VERSION OF LIMIT THEOREM

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 239 - 247
Copyright
Copyright © Applied Probability Trust 1975 

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References

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