Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T13:47:47.338Z Has data issue: false hasContentIssue false
  • English
  • Français

Almost sure asymptotic likelihood theory for diffusion processes

Published online by Cambridge University Press:  14 July 2016

T. S. Lee  and
F. Kozin
T. S. Lee
Affiliation:
Polytechnic Institute of New York
F. Kozin
Affiliation:
Polytechnic Institute of New York
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider maximum likelihood estimators for parameters of diffusion processes that are generated by nth-order Ito equations. We establish asymptotic consistency as well as convergence in distribution to normality for the estimators. Examples are presented and discussed.

Keywords

STOCHASTIC EQUATIONSITO EQUATIONSDIFFUSION PROCESSESMAXIMUM LIKELIHOOD ESTIMATORSCONSISTENT ESTIMATORSASYMPTOTIC NORMALITYRADON–NIKODYM DERIVATIVESSTATIONARITYERGODICITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 527 - 537
Copyright
Copyright © Applied Probability Trust 1977 

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] Brown, B. M. and Hewitt, J. I. (1975) Asymptotic likelihood theory for diffusion processes. J. Appl. Prob. 12, 228–238.CrossRefGoogle Scholar
[2] Wonham, W. M. (1966) Liapunov criteria for weak stochastic stability. J. Differential Equations 2, 195–207.CrossRefGoogle Scholar
[3] Khazminskii, R. Z. (1969) Stability of Systems of Differential Equations under Random Disturbances of Their Parameters. (Russian), Nauka, Moscow.Google Scholar
[4] Khazminskii, R. Z. (1960) Ergodic properties of recurrent diffusion processes and stabilization of the solution to the Cauchy problem for parabolic equations. Theor. Prob. Appl. 5, 179–196.Google Scholar
[5] Lee, T. S. and Kozin, F. (1976) Consistency of maximum likelihood estimators for a class of non-stationary models. Proceedings of the 9th Hawaii International Conference on System Sciences, Honolulu, January 1976, 187–189.Google Scholar
[6] Duncan, T. E. (1968) Evaluation of likelihood functions. Inf. and Control 13, 62–74.Google Scholar
[7] Wong, E. (1971) Stochastic Processes in Information and Dynamical Systems. McGraw-Hill, New York.Google Scholar
[8] 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
[9] 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