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Random collision processes and their limiting distribution using the discrimination information

Published online by Cambridge University Press:  14 July 2016

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

By analogy with statistical mechanics random collision processes are considered. In two cases we derive their limiting distributions using discrimination information. In one case the limiting distribution is unique and in the other one the family of limiting distributions is an exponential family.

Keywords

RANDOM COLLISION PROCESSDISCRIMINATION INFORMATIONBOLTZMANN'S H-THEOREMEXPONENTIAL FAMILYDETERMINISTIC RANDOM MATING
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 266 - 280
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Feller, W. (1968) An Introduction to Probability Theory and its Applications. Vol. 1, 3rd. ed. John Wiley, New York.Google Scholar
[2] Kesten, H. (1970) Quardatic transformations: a model for population growth. I, II. Adv. Appl. Prob. 2, 1–82, 179–228.CrossRefGoogle Scholar
[3] Kullback, S. (1959) Information Theory and Statistics. John Wiley, New York.Google Scholar
[4] Kullback, S. (1966) An information-theoretic derivation of certain limit relations for a stationary Markov chain. SIAM J. Control 4, 454–459.CrossRefGoogle Scholar
[5] Moran, P. A. P. (1961) Entropy, Markov processes and Boltzmann's H-theorem. Proc. Camb. Phil. Soc. 57, 833–842.CrossRefGoogle Scholar
[6] Moran, P. A. P. (1962) The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.Google Scholar
[7] Rényi, A. (1961) On measures of entropy and information. Proc. Fourth Berkeley Sympposium I, 547–561.Google Scholar