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Estimating the law of randomly moving particles by counting

Published online by Cambridge University Press:  14 July 2016

Philip McDunnough
Philip McDunnough*
Affiliation:
University of Toronto
*
∗Postal address: Department of Statistics, University of Toronto, Toronto, Ontario, Canada M5S1A1.
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Abstract

The fluctuation of the counts of particles in m regions are used to yield an estimate of a fundamental motion parameter. The effect of varying m on the precision of the estimation method is considered. An exact analysis and simulation of the Fürth pedestrian vector process is presented.

Keywords

PARTICLE FLUCTUATIONPOINT PROCESSSTATISTICAL PHYSICSVARIATE- DIFFERENCES
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 25 - 35
Copyright
Copyright © Applied Probability Trust 1979 

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References

Bartlett, M. S. (1950) Recurrence times. Nature, London 165, 727.CrossRefGoogle ScholarPubMed
Bartlett, M. S. (1966) Introduction to Stochastic Processes, 2nd edn. Cambridge University Press.Google Scholar
Brillinger, D. R. (1975) Time Series, Data Analysis and Theory. Holt, Rinehart and Winston, New York.Google Scholar
Fürth, R. (1918) Statistik und Wahrscheinlichkeitsnachwirkung. Phys. Zeit. 19, 421–426.Google Scholar
Fürth, R. (1919) Statistik und Wahrscheinlichkeitsnachwirkung. Phys. Zeit. 20, 21.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
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
Lindley, D. V. (1954) The estimation of velocity distributions from counts. Proc. Internat. Congr. Mathematicians, Amsterdam 3, 427–444.Google Scholar
McDunnough, P. (1977) The Smoluchowski Process in Statistical Physics and Related Topics. Ph. D. Thesis, McGill University, Montreal.Google Scholar
McDunnough, P. (1978) Some aspects of the Smoluchowski process. J. Appl. Prob. 15, 663–674.CrossRefGoogle Scholar
Rothschild, Lord (1953) A new method of measuring the activity of spermatozoa. J. Experimental Biol. 30, 178–199.Google Scholar
Ruben, H. (1962) Some aspects of the emigration–immigration process. Ann. Math. Statist. 33, 111–129.Google Scholar
Ruben, H. (1963) The estimation of a fundamental interaction parameter in an emigration–immigration process. Ann. Math. Statist. 34, 238–259.Google Scholar
Ruben, H. (1964) Generalized concentration fluctuations under diffusion equilibrium. J. Appl. Prob. 1, 47–68.CrossRefGoogle Scholar
Ruben, H. and Rothschild, Lord (1953) Estimation of mean speeds of organisms and particles by counting. Unpublished.Google Scholar
Smoluchowski, M. V. (1916) Drei Vorträge über Diffusion, Brownsche Bewegung und Koagulaion von Kolloidteilchen. Phys. Zeit. 17, 557–585.Google Scholar