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Asymptotic likelihood theory for diffusion processes

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

We investigate the large-sample behaviour of maximum likelihood estimates (MLE's) of the parameters of a diffusion process, which is observed throughout continuous time. The results (limit normal distribution for the MLE and an asymptotic chi-squared likelihood ratio test) correspond exactly to classical asymptotic likelihood results, and follow easily from a central limit theorem for stochastic integrals.

Keywords

DIFFUSION PROCESSESMAXIMUM LIKELIHOOD ESTIMATESBROWNIAN MOTIONSTATIONARITYERGODICITYSTOCHASTIC INTEGRALSRADON-NIKODYM DERIVATIVESMARTINGALE CENTRAL LIMIT THEOREMLIKELIHOOD RATIO TEST
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 228 - 238
Copyright
Copyright © Applied Probability Trust 1975 

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References

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