Identification of dynamical systems with small noise
Author(s)
Bibliographic Information
Identification of dynamical systems with small noise
（Mathematics and its applications, v. 300）
Kluwer Academic Publishers, c1994
Available at / 33 libraries
-
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:519.2/k9692070308467
-
No Libraries matched.
- Remove all filters.
Note
Bibliography: p. 289-296
Includes index
Description and Table of Contents
Description
Small noise is a good noise. In this work, we are interested in the problems of estimation theory concerned with observations of the diffusion-type process Xo = Xo, 0 ~ t ~ T, (0. 1) where W is a standard Wiener process and St(') is some nonanticipative smooth t function. By the observations X = {X , 0 ~ t ~ T} of this process, we will solve some t of the problems of identification, both parametric and nonparametric. If the trend S(-) is known up to the value of some finite-dimensional parameter St(X) = St((}, X), where (} E e c Rd , then we have a parametric case. The nonparametric problems arise if we know only the degree of smoothness of the function St(X), 0 ~ t ~ T with respect to time t. It is supposed that the diffusion coefficient c is always known. In the parametric case, we describe the asymptotical properties of maximum likelihood (MLE), Bayes (BE) and minimum distance (MDE) estimators as c --+ 0 and in the nonparametric situation, we investigate some kernel-type estimators of unknown functions (say, StO,O ~ t ~ T). The asymptotic in such problems of estimation for this scheme of observations was usually considered as T --+ 00 , because this limit is a direct analog to the traditional limit (n --+ 00) in the classical mathematical statistics of i. i. d. observations. The limit c --+ 0 in (0. 1) is interesting for the following reasons.
Table of Contents
Introduction. 1. Auxiliary Results. 2. Asymptotic Properties of Estimator in Standard and Nonstandard Situations. 3. Expansions. 4. Nonparametric Estimation. 5. The Disorder Problem. 6. Partially Observed Systems. 7. Minimum Distance Estimation. Remarks. References. Index.
by "Nielsen BookData"
