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Notes on “Estimation theory for growth and immigration rates in a multiplicative process”

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde  and
E. Seneta
C. C. Heyde
Affiliation:
Australian National University, Canberra
E. Seneta
Affiliation:
Australian National University, Canberra
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Abstract

Some minor corrections to Heyde and Seneta (1972) are made, and new convergence rate results given. Estimation by recurrence methods is discussed, as announced earlier.

Keywords

ESTIMATION THEORYGROWTH AND IMMIGRATION RATESMULTIPLICATIVE PROCESSESSTRONG CONSISTENCYSTRONG LAWMARTINGALESCENTRAL LIMIT THEOREMFIRST ORDER AUTOREGRESSIONPARTICLE FLUCTUATIONLINDEBERG CONDITIONLAW OF ITERATED LOGARITHMSMOLUCHOWSKI PROCESSRECURRENCE ESTIMATION METHODS
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 572 - 577
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Bartlett, M. S. (1955) An Introduction to Stochastic Processes. Cambridge University Press, Cambridge.Google Scholar
[2] Heyde, C. C. and Scott, D. J. (1973) Invariance principles for the law of the iterated logarithm for martingales and processes with stationary increments. Ann. Probab. 1, 428–436.Google Scholar
[3] Heyde, C. C. and Seneta, E. (1972) Estimation theory for growth and immigration rates in a multiplicative process. J. Appl. Prob. 9, 235–256.Google Scholar
[4] Kac, M. (1959) Probability and Related Topics in Physical Sciences. Interscience, London.Google Scholar
[5] Lindley, D. V. (1954). The estimation of velocity distributions from counts. Proc, Int. Congress of Mathematicians (Amsterdam) 3, 427–444.Google Scholar
[6] Neveu, J. (1965) Mathematical Foundations of the Calculus of Probability. Holden-Day, San Francisco.Google Scholar
[7] Ruben, H. (1964) Generalized concentration fluctuations under diffusion equilibrium. J. Appl. Prob. 1, 47–68.Google Scholar