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Inference for the diffusion branching process

Published online by Cambridge University Press:  14 July 2016

B. M. Brown  and
J. I. Hewitt
B. M. Brown
Affiliation:
University of Cambridge
J. I. Hewitt
Affiliation:
University of Cambridge
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Abstract

For the diffusion branching process, we consider a method of inference that is essentially sequential in nature. The method allows us to simplify the natural sufficient statistics involved, and we are able to get their distributions quite easily by translating our problem into a standard problem in Brownian motion. Under certain circumstances, we are left with a complete sufficient statistic whose distribution belongs to an exponential family, and can therefore derive minimum variance unbiased estimators, etc.

Keywords

INFERENCE FOR STOCHASTIC PROCESSESDIFFUSION PROCESSBRANCHING PROCESSBROWNIAN MOTIONMINIMUM VARIANCE UNBIASED ESTIMATION

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 588 - 594
Copyright
Copyright © Applied Probability Trust 1975 

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