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A note on functions of Markov processes with an application to a sequence of χ2 statistics

Published online by Cambridge University Press:  14 July 2016

Murray A. Cameron
Murray A. Cameron*
Affiliation:
Csiro Division of Mathematical Statistics, Newtown, N.S.W.
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Abstract

A sufficient condition for a function of a Markov process to be Markovian is obtained by considering a reverse process of the original Markov process. An application of this result provides a simple derivation of the joint distribution of a sequence of Pearson χ2 statistics previously obtained by Zaharov, Sarmanov and Sevast'ianov (1969).

Keywords

FUNCTIONS OF MARKOV PROCESSESREVERSE PROCESSESSEQUENTIAL PEARSON χ2
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 895 - 900
Copyright
Copyright © Applied Probability Trust 1973 

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References

Burke, C. J. and Rosenblatt, M. (1958) A Markovian function of a Markov chain. Ann. Math. Statist. 29, 1112–1122.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications. Vol. II, 2nd Edition. John Wiley, New York.Google Scholar
Griffiths, R. C. (1970) Infinitely divisible multivariate gamma distributions. Sankhya A 32, 393–404.Google Scholar
Kibble, W. F. (1941) A two-variate gamma type distribution. Sankhya 5, 137–150.Google Scholar
Miller, K. S. (1964) Multidimensional Gaussian Distributions. John Wiley, New York.Google Scholar
Rosenblatt, M. (1959) Functions of a Markov process that are Markovian. J. Math. Mech. 8, 585–596.Google Scholar
Rosenblatt, M. (1966) Functions of a Markov process. Zeit. Wahrscheinlichkeitsth. 5, 232–243.Google Scholar
Zaharov, V. K., Sarmanov, O. V. and Sevast'Ianov, B. A. (1969) A sequential χ 2 test. (In Russian) Mat. Sb. 79 (121), 444–460.Google Scholar