Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-12T14:22:52.646Z Has data issue: false hasContentIssue false
  • English
  • Français

Random collision processes with transition probabilities belonging to the same type of distribution

Published online by Cambridge University Press:  14 July 2016

Shōichi Nishimura
Shōichi Nishimura*
Affiliation:
Tokyo Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

By analogy with statistical mechanics we consider a random collision process with discrete time wand continuous states x ∈ [0, ∞). We assume three conditions (i), (ii) and (iii), which can be applied to Kac's model of a Maxwellian gas, and show that the sequence of probability distributions converges to a probability distribution using their moments.

Keywords

RANDOM COLLISION PROCESSMOMENTCHARACTERISTIC FUNCTIONKAC'S MODEL OF A MAXWELLIAN GAS
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 703 - 714
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. (1957) An Introduction to Probability Theory and its Applications. Vol. I, 2nd ed. John Wiley, New York.Google Scholar
[2]Ikenberry, E. and Truesdell, C. (1956) On the pressures and the flux of energy in a gas according to Maxwell's kinetic theory, I. J. Rational Mech. Anal. 5, 1–128.Google Scholar
[3]Kac, M. (1959) Probability and Related Topics in Physical Sciences. International Publishers, London.Google Scholar
[4]Lukacs, E. (1970) Characteristic Functions. 2nd ed. Griffin, London.Google Scholar
[5]Mckean, H. (1966) Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas. Arch. Rational Mech. Anal. 21, 343–367.Google Scholar
[6]Moran, P. A. P. (1961) Entropy, Markov process and Boltzmann's H-theorem. Proc. Camb. Phil. Soc. 57, 833–842.Google Scholar
[7]Nishimura, S. (1974) Random collision processes and their limiting distribution using the discrimination information. J. Appl. Prob. 11, 266–280.Google Scholar