Skip to main content
×
×
Home

Almost sure asymptotic likelihood theory for diffusion processes

  • T. S. Lee (a1) and F. Kozin (a1)
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.

Copyright
References
Hide All
[1] Brown, B. M. and Hewitt, J. I. (1975) Asymptotic likelihood theory for diffusion processes. J. Appl. Prob. 12, 228238.
[2] Wonham, W. M. (1966) Liapunov criteria for weak stochastic stability. J. Differential Equations 2, 195207.
[3] Khazminskii, R. Z. (1969) Stability of Systems of Differential Equations under Random Disturbances of Their Parameters. (Russian), Nauka, Moscow.
[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, 179196.
[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, 187189.
[6] Duncan, T. E. (1968) Evaluation of likelihood functions. Inf. and Control 13, 6274.
[7] Wong, E. (1971) Stochastic Processes in Information and Dynamical Systems. McGraw-Hill, New York.
[8] Kailath, T. and Zakai, M. (1971) Absolute continuity and Radon-Nikodym derivatives for certain measures relative to Wiener measure. Ann. Math. Statist. 42, 130140.
[9] Brown, B. M. and Eagleson, G. K. (1971) Martingale convergence to infinitely divisible laws with finite variances. Trans. Amer. Math. Soc. 162, 449453.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 77 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th September 2018. This data will be updated every 24 hours.