Random fields estimation theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman Scientific & Technical u.a.
1990
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
48 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 273 S. |
| ISBN: | 0470214813 0582037689 |
Staff View
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Record in the Search Index
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| adam_text | Table of Contents
Preface vii
I. Introduction 1
II. Formulation of basic results 7
§1. Statement of the problem 7
§2. Formulation of the results (multidimensional case) 11
§3. Formulation of the results (one dimensional case) 15
§4. Examples of kernels of class Of and solutions to the basic
equation 21
§5. Formula for the error of the optimal estimate 24
III. Numerical solution of the basic integral equation in
distributions 27
§1. Basic ideas 27
§2. Theoretical approaches 30
§3. Multidimensional equation 36
§4. Numerical solution based on the approximation of the
kernel 39
§5. Asymptotic behaviour of the optimal filter as the white noise
component goes to zero 46
§6. A general approach 48
IV. Proofs 54
§1. Proof of Theorem II.2.1 54
§2. Proof of Theorem II.2.2 61
§3. Proof of Theorems II.3.1 and II.3.2 66
§4. Another approach 71
vi CONTENTS
V. Applications 72
§1. What is the optimal size of the domain on which the data are
to be collected? 72
§2. Discrimination of random fields against noisy background 74
§3. Quasioptimal estimates of derivatives of random
functions 81
§4. Stable summation of orthogonal series and integrals with
randomly perturbed coefficients 92
§5. Resolution ability of linear systems 95
§6. Ill posed problems and estimation theory 106
§7. A remark on nonlinear (polynomial) estimates 134
VI. Auxiliary results 137
§1. Sobolev spaces and distributions 137
§2. Eigenfunctions expansions for elliptic self adjoint
operators 145
§3. Asymptotics of the spectrum of linear operators 161
§4. Elements of probability theory 197
Appendix: Estimation and scattering theory 219
Research problems 262
Bibliographical notes 263
References 266
List of symbols 272
Subject index 274
|
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| id | DE-604.BV004174673 |
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| indexdate | 2024-07-09T16:09:27Z |
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| isbn | 0470214813 0582037689 |
| language | English |
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| physical | VII, 273 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Longman Scientific & Technical u.a. |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Ramm, Alexander G. Verfasser aut Random fields estimation theory A. G. Ramm 1. publ. Harlow, Essex Longman Scientific & Technical u.a. 1990 VII, 273 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 48 Champs aléatoires ram Estimation Estimation, Théorie de l' ram Estimation theory Random fields Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Schätztheorie (DE-588)4121608-8 gnd rswk-swf Zufälliges Feld (DE-588)4191094-1 s Schätztheorie (DE-588)4121608-8 s DE-604 Pitman monographs and surveys in pure and applied mathematics 48 (DE-604)BV000022446 48 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002602699&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ramm, Alexander G. Random fields estimation theory Pitman monographs and surveys in pure and applied mathematics Champs aléatoires ram Estimation Estimation, Théorie de l' ram Estimation theory Random fields Zufälliges Feld (DE-588)4191094-1 gnd Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4191094-1 (DE-588)4121608-8 |
| title | Random fields estimation theory |
| title_auth | Random fields estimation theory |
| title_exact_search | Random fields estimation theory |
| title_full | Random fields estimation theory A. G. Ramm |
| title_fullStr | Random fields estimation theory A. G. Ramm |
| title_full_unstemmed | Random fields estimation theory A. G. Ramm |
| title_short | Random fields estimation theory |
| title_sort | random fields estimation theory |
| topic | Champs aléatoires ram Estimation Estimation, Théorie de l' ram Estimation theory Random fields Zufälliges Feld (DE-588)4191094-1 gnd Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Champs aléatoires Estimation Estimation, Théorie de l' Estimation theory Random fields Zufälliges Feld Schätztheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002602699&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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