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First-Order Conservative Processes with Multiple Latent Roots

Published online by Cambridge University Press:  14 July 2016

J. Radcliffe  and
P. J. Staff
J. Radcliffe
Affiliation:
University of Leeds
P. J. Staff
Affiliation:
University of New South Wales
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Extract

There are now many examples in various fields where the behaviour of ‘particles' as exhibited by their transition from one state to another is described by a multidimensional stochastic process. The linear migration model in which particles move independently of one another through a number of states has been dealt with by Bartlett (1949). This process has been used by Siegert (1949) in considering the approach to equilibrium of non-interacting gas molecules and by Krieger and Gans (1960) and Gans (1960) to examine the distribution of a multicomponent system disturbed from its equilibrium distribution and relaxing by first-order processes to another equilibrium. The correspondence between the deterministic model based on the principle of mass action and the stochastic model has been discussed by Darvey and Staff (1966) in the context of unimolecular multicomponent chemical reactions.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 186 - 194
Copyright
Copyright © Applied Probability Trust 

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References

Bartholomew, D. J. (1967) Stochastic Models for Social Processes. J. Wiley and Sons, London.Google Scholar
Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211–229.Google Scholar
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar
Darvey, I. G. and Staff, P. J. (1966) Stochastic approach to first-order chemical reaction kinetics. J. Chem. Phys. 44, 990–997.Google Scholar
Gans, P. J. (1960) Open first-order stochastic processes. J. Chem. Phys. 33, 691–694.Google Scholar
Gantmacher, F. R. (1959) The Theory of Matrices. Chelsea Publ. Co., New York.Google Scholar
Krieger, I. M. and Gans, P. J. (1960) First-order stochastic processes. J. Chem. Phys. 32, 247–250.Google Scholar
Ledermann, W. (1950) On the asymptotic probability distribution for certain Markoff processes. Proc. Camb. Phil. Soc. 46, 581–594.Google Scholar
Ledermann, W. (1951) Corrigendum to the paper on the asymptotic probability distribution for certain Markoff processes. Proc. Camb. Phil. Soc. 47, 626.Google Scholar
Mcquarrie, D. A. (1967) Stochastic approach to chemical kinetics. J. Appl. Prob. 4, 413–478.Google Scholar
Siegert, A. J. F. (1949) On the approach to statistical equilibrium. Phys. Rev. 76, 1708–1714.Google Scholar