<電子ブック>
Stochastic and Integral Geometry / by Rolf Schneider, Wolfgang Weil
(Probability and Its Applications)
版 | 1st ed. 2008. |
---|---|
出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 2008 |
本文言語 | 英語 |
大きさ | XII, 694 p : online resource |
著者標目 | *Schneider, Rolf author Weil, Wolfgang author SpringerLink (Online service) |
件 名 | LCSH:Probabilities LCSH:Convex geometry LCSH:Discrete geometry FREE:Probability Theory FREE:Convex and Discrete Geometry |
一般注記 | Foundations of Stochastic Geometry -- Prolog -- Random Closed Sets -- Point Processes -- Geometric Models -- Integral Geometry -- Averaging with Invariant Measures -- Extended Concepts of Integral Geometry -- Integral Geometric Transformations -- Selected Topics from Stochastic Geometry -- Some Geometric Probability Problems -- Mean Values for Random Sets -- Random Mosaics -- Non-stationary Models -- Facts from General Topology -- Invariant Measures -- Facts from Convex Geometry Stochastic geometry has in recent years experienced considerable progress, both in its applications to other sciences and engineering, and in its theoretical foundations and mathematical expansion. This book, by two eminent specialists of the subject, provides a solid mathematical treatment of the basic models of stochastic geometry -- random sets, point processes of geometric objects (particles, flats), and random mosaics. It develops, in a measure-theoretic setting, the integral geometry for the motion and the translation group, as needed for the investigation of these models under the usual invariance assumptions. A characteristic of the book is the interplay between stochastic and geometric arguments, leading to various major results. Its main theme, once the foundations have been laid, is the quantitative investigation of the basic models. This comprises the introduction of suitable parameters, in the form of functional densities, relations between them, and approaches to their estimation. Much additional information on stochastic geometry is collected in the section notes. As a combination of probability theory and geometry, the volume is intended for readers from either field. Probabilists with interest in random spatial structures, or motivated by the prospect of applications, will find an in-depth presentation of the geometric background. Geometers can see integral geometry "at work" and may be surprised to learn how classical results from convex geometry have elegant applications in a stochastic setting HTTP:URL=https://doi.org/10.1007/978-3-540-78859-1 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9783540788591 |
|
電子リソース |
|
EB00229583 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:QA273.A1-274.9 DC23:519.2 |
書誌ID | 4000117670 |
ISBN | 9783540788591 |
類似資料
この資料の利用統計
このページへのアクセス回数:2回
※2017年9月4日以降