Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-30T21:15:36.997Z Has data issue: false hasContentIssue false
  • English
  • Français

On estimating the diffusion coefficient

Published online by Cambridge University Press:  14 July 2016

Gejza Dohnal
Gejza Dohnal*
Affiliation:
Technical University of Prague
*
∗Postal address: Department of Mathematics and Descriptive Geometry, Faculty of Engineering, Technical University of Prague, Suchbatarova 4, Prague 16607, Czechoslovakia.
Get access Rights & Permissions [Opens in a new window]

Abstract

Random processes of the diffusion type have the property that microscopic fluctuations of the trajectory make possible the identification of certain statistical parameters from one continuous observation. The paper deals with the construction of parameter estimates when observations are made at discrete but very dense time points.

Keywords

DIFFUSION PROCESSESPARAMETER ESTIMATIONLOCAL ASYMPTOTIC MIXED NORMALITYDISCRETE OBSERVATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 105 - 114
Copyright
Copyright © Applied Probability Trust 1987 

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

Arató, M. (1978) On the statistical examination of continuous state Markov processes I, II. Select. Trans. Math. Statist. Prob. 14, 203–251.Google Scholar
Brown, B. M. (1971) Martingale central limit theorems. Ann. Math. Statist. 42, 59–66.10.1214/aoms/1177693494Google Scholar
Dacunha-Castelle, D. and Florens-Zmirou, D. (1984) Time-discretization effect for the estimation of the parameter of a differential stochastic equation. Université de Paris-Sud. Prepublication.Google Scholar
Hájek, J. (1972) Local asymptotic minimax and admissibility in estimation. Proc. 6th Berkeley Symp. Math. Statist. Prob. 1, 175–194.Google Scholar
Jeganathan, P. (1981) On a decomposition of the limit distribution of a sequence of estimators. Sankhya A 43, 26–36.Google Scholar
Jeganathan, P. (1982) On the asymptotic theory of estimation when the limit of the log-likelihood ratios is mixed normal. Sankhya A 44, 173–212.Google Scholar
Jeganathan, P. (1983) Some properties of risk functions in estimation when the limit of the experiment is mixed normal. Sankhya A 45, 66–86.Google Scholar
Le Cam, L. (1960) Locally asymptotically normal families of distributions. Univ. Calif. Publ. Statist. 3, 37–98.Google Scholar
Le Cam, L. (1972) Limits of experiments. Proc. 6th Berkeley Symp. Math. Statist. Prob. 1, 245–261.Google Scholar
Prakasa Rao, B. L. S. and Rubin, H. (1981) Asymptotic theory of estimation in nonlinear stochastic differential equations. Sankhya A 43, 170–189.Google Scholar
Swansen, A. R. (1983) A note on asymptotic inference in a class of non-stationary processes. Stoch. Proc. Appl. 15, 181–191.Google Scholar