Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T17:45:20.716Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimum contrast estimation in diffusion processes

Published online by Cambridge University Press:  14 July 2016

Vĕra Lánska
Vĕra Lánska*
Affiliation:
Institute of Information Theory and Automation, Czechoslovak Academy of Sciences
*
∗Postal address: Institute of Information Theory and Automation, Czechoslovak Academy of Sciences, 18076 Prague 8, Pod vodárenskou vĕž í4, Czechoslovakia.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is concerned with the asymptotic theory of estimates of an unknown parameter in continuous-time Markov processes, which are described by non-linear stochastic differential equations. The maximum likelihood estimate and the minimum contrast estimate are investigated. For these estimates strong consistency and asymptotic normality are proved. The unknown parameter is assumed to take its values either in an open or in a compact set of real numbers.

Keywords

CONTINUOUS-TIME STOCHASTIC PROCESSMAXIMUM LIKELIHOOD FUNCTIONMINIMUM CONTRAST FUNCTIONESTIMATEASYMPTOTIC BEHAVIOUR
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 65 - 75
Copyright
Copyright © Applied Probability Trust 1979 

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

Brown, B. M. and Hewitt, J. I. (1975) Asymptotic likelihood theory for diffusion processes. J. Appl. Prob. 12, 228–238.Google Scholar
Dufková, V. (1977) On controlled one-dimensional diffusion processes with unknown parameter. Adv. Appl. Prob. 9, 105–124.Google Scholar
Feigin, P. D. (1976) Maximum likelihood estimation for continuous-time stochastic processes. Adv. Appl. Prob. 8, 712–736.Google Scholar
Gänssler, P. (1972) Note on minimum contrast estimates for Markov processes. Metrika 19, 115–130.Google Scholar
Mandl, P. (1968) Analytical Treatment of One-Dimensional Markov Processes. Academia, Prague; Springer–Verlag, Berlin.Google Scholar
McKean, H. P. (1969) Stochastic Integrals. Academic Press, New York.Google Scholar
Meyer, P. A. (1966) Probability and Potentials. Blaisdell, Waltham, Mass.Google Scholar
Pfanzagl, J. (1969) On the measurability and consistency of minimum contrast estimates. Metrika 14, 249–272.Google Scholar