Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T13:52:55.803Z Has data issue: false hasContentIssue false

Random collision processes and their limiting distribution using the discrimination information

Published online by Cambridge University Press:  14 July 2016

Shōichi Nishimura*
Affiliation:
Tokyo Institute of Technology

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1974 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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, 182, 179228.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, 454459.CrossRefGoogle Scholar
[5] Moran, P. A. P. (1961) Entropy, Markov processes and Boltzmann's H-theorem. Proc. Camb. Phil. Soc. 57, 833842.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, 547561.Google Scholar