portada Identification of Dynamical Systems with Small Noise (en Inglés)

Identification of Dynamical Systems with Small Noise (en Inglés)

Formato

Libro Físico

Autor

Yury A. Kutoyants

Editorial

Springer

Idioma

Inglés

N° páginas

301

Encuadernación

Tapa Blanda

Dimensiones

23.4x15.6x1.7 cm

Peso

0.44 kg.

ISBN13

9789401044448

Categorías

Cibernética y teoría de sistemas
Probabilidad y estadística
Matemáticas aplicadas

Identification of Dynamical Systems with Small Noise (en Inglés)

Yury A. Kutoyants (Autor) · Springer · Tapa Blanda

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Reseña del libro "Identification of Dynamical Systems with Small Noise (en Inglés)"

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.