Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-21T18:57:38.329Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Billingsley, P. (1961) Statistical methods in Markov Chains. Ann. Math. Statist. 32, 12–40.Google Scholar
[2] Billingsley, P. (1961) Statistical Inference for Markov Processes. University of Chicago Press.Google Scholar
[3] Breiman, L. (1968) Probability. Addison-Wesley, Reading, Mass.Google Scholar
[4] Brown, B. M. and Eagleson, G. K. (1971) Martingale convergence to infinitely divisible laws with finite variances. Trans. Amer. Math. Soc. 162, 449–453.Google Scholar
[5] Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
[6] Gikhman, I. and Skorokhod, A. (1972) Stochastic Differential Equations. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[7] Kailath, T. and Zakai, M. (1971) Absolute continuity and Radon-Nikodym derivatives for certain measures relative to Wiener measure. Ann. Math. Statist. 42, 130–140.Google Scholar
[8] Mckean, H. P. (1968) Stochastic Integrals. Academic Press, New York.Google Scholar
[9] Scott, D. J. (1973) Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach. Adv. Appl. Prob. 5,119–137.CrossRefGoogle Scholar