{"product_id":"identification-of-dynamical-systems-with-small-noise-von-yury-a-kutoyants","title":"Identification of Dynamical Systems with Small Noise","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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792330530\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789401044448\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780792330530","offer_id":51066849350,"sku":"9780792330530","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9789401044448","offer_id":39415323295837,"sku":"9789401044448","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/876e4834-afb3-429a-89ae-1a8e1df608d3.jpg?v=1772176471","url":"https:\/\/shop.autorenwelt.de\/products\/identification-of-dynamical-systems-with-small-noise-von-yury-a-kutoyants","provider":"Autorenwelt Shop","version":"1.0","type":"link"}