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A central limit theorem for linear Kolmogorov's birth-growth models

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  • Chiu, S. N.

Abstract

A Poisson process in space-time is used to generate a linear Kolmogorov's birth-growth model. Points start to form on [0,L] at time zero. Each newly formed point initiates two bidirectional moving frontiers of constant speed. New points continue to form on not-yet passed over parts of [0,L]. The whole interval will eventually be passed over by the moving frontiers. Let NL be the total number of points formed. Quine and Robinson (1990) showed that if the Poisson process is homogeneous in space-time, the distribution of (NL - E[NL])/[radical sign]var[NL] converges weakly to the standard normal distribution. In this paper a simpler argument is presented to prove this asymptotic normality of NL for a more general class of linear Kolmogorov's birth-growth models.

Suggested Citation

  • Chiu, S. N., 1997. "A central limit theorem for linear Kolmogorov's birth-growth models," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 97-106, February.
    • Handle: RePEc:eee:spapps:v:66:y:1997:i:1:p:97-106
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    1. Quine, M. P. & Robinson, J., 1992. "Estimation for a linear growth model," Statistics & Probability Letters, Elsevier, vol. 15(4), pages 293-297, November.
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    Cited by:

    1. S. N. Chiu & M. P. Quine & M. Stewart, 2000. "Nonparametric and Parametric Estimation for a Linear Germination-Growth Model," Biometrics, The International Biometric Society, vol. 56(3), pages 755-760, September.
    2. Erhardsson, Torkel, 2001. "Refined distributional approximations for the uncovered set in the Johnson-Mehl model," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 243-259, December.

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    1. S. N. Chiu & M. P. Quine & M. Stewart, 2000. "Nonparametric and Parametric Estimation for a Linear Germination-Growth Model," Biometrics, The International Biometric Society, vol. 56(3), pages 755-760, September.

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