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On joint exchangeability and conservative processes with stochastic rates

Published online by Cambridge University Press:  14 July 2016

Roy Saunders
Roy Saunders*
Affiliation:
Northern Illinois University
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Abstract

In a previous article Saunders (1975) investigated the form of transition probabilities for a generalization of conservative processes in which the usual transition rate parameters are replaced by time-dependent stochastic variables. The results of that investigation are given in terms of properties of exchangeable random variables and require that the process be in a particular initial state at time zero. This article removes the restriction on the initial state by using some properties of two sequences of jointly exchangeable variables. General results analogous to those obtained previously are shown to hold for general initial states.

Keywords

CONSERVATIVE PROCESSSTOCHASTIC RATESCOMPARTMENT MODELSJOINTLY EXCHANGEABLE RANDOM VARIABLESPROCESSES UNDER THE INFLUENCE OF ANOTHER PROCESSMULTIDIMENSIONAL CONSERVATIVE PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 584 - 590
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211–229.Google Scholar
[2] Blum, J. R. Chernoff, H., Rosenblatt, M. and Tiecher, H. (1958) Central limit theorems for interchangeable processes. Canad. J. Math. 10, 222–229.Google Scholar
[3] Feller, W. (1965) An Introduction to Probability Theory and its Applications, Volume II. Wiley, New York.Google Scholar
[4] Loève, M. (1963) Probability Theory. Van Nostrand, Princeton, N.J.Google Scholar
[5] Matis, J. H. and Hartley, H. O. (1971) Stochastic compartment analysis model and least squares estimation from time series data. Biometrics 27, 77–102.Google Scholar
[6] Puri, P. S. (1972) A method of studying the integral functionals of stochastic processes with applications III. Proc. 6th Berkeley Symp. Math. Statist. Prob. 3, 481–500.Google Scholar
[7] Puri, P. S. (1974) A stochastic process under the influence of another arising in the theory of epidemics. Proc. I.M.S. Summer Research Inst. on Statist. Influence for Stochastic Processes. (To appear.) Google Scholar
[8] Kryscio, R. J. and Saunders, R. (1975) Parameter estimation for the carrier-borne epidemic model. (Unpublished research report.) Google Scholar
[9] Saunders, R. (1975) Conservative processes with stochastic rates. J. Appl. Prob. 12, 447–456.CrossRefGoogle Scholar
[10] Schach, S. (1971) Weak convergence results for a class of multivariate Markov processes. Ann. Math. Statist. 42, 451–465.Google Scholar
[11] Severo, N. C. (1970) A note on the Ehrenfest multiurn model. J. Appl. Prob. 7, 444–445.CrossRefGoogle Scholar
[12] Thakur, A. K., Rescigno, A. and Shafer, D. E. (1973) On the stochastic theory of compartments. Bull. Math. Biol. 35, 263–271.Google Scholar
[13] Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–490.CrossRefGoogle ScholarPubMed