Adaptive algorithms and stochastic approximations:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer-Verl.
[2012]
|
| Edition: | Softcover repr. of the hardcover 1. ed. 1990 |
| Series: | Stochastic modelling and applied probability
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 364 S. |
| ISBN: | 3642758967 9783642758966 |
Staff View
MARC
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| 100 | 1 | |a Benveniste, Albert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Adaptive algorithms and stochastic approximations |c Alvert Benveniste ; Michel Metivier ; Pierre Priouret |
| 250 | |a Softcover repr. of the hardcover 1. ed. 1990 | ||
| 264 | 1 | |a Berlin |b Springer-Verl. |c [2012] | |
| 300 | |a XII, 364 S. | ||
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Record in the Search Index
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Contents
Introduction 1
Part I. Adaptive Algorithms: Applications 7
1. General Adaptive Algorithm Form 9
1.1 Introduction .9
1.2 Two Basic Examples and Their Variants . 10
1.3 General Adaptive Algorithm Form and Main Assumptions .23
1A Problems Arising . 29
1.5 Summary of the Adaptive Algorithm Form: Assumptions (A) . .31
1.6 Conclusion . 33
1.7 Exercises. o. 34
1.8 Comments on the Literature . 38
2. Convergence: the ODE Method 40
2.1 Introduction . 40
2.2 Mathematical Tools: Informal Introduction . 41
2.3 Guide to the Analysis of Adaptive Algorithms.48
2.4 Guide to Adaptive Algorithm Design.55
2.5 The Transient Regime .75
2.6 Conclusion . 76
2.7 Exercises. 76
2.8 Comments on the Literature.100
3.
Rate of Convergence
3.1 Mathematical Tools: Informal Description .
3.2 Applications to the Design of Adaptive Algorithms
Decreasing Gain.
3.3 Conclusions from Section 3.2
3.4 Exercises.
3.5 Comments on the Literature
103
103
no
116
116
118
X
Contents
4. Tracking Non-Stationary Parameters 120
4.1 Tracking Ability of Algorithms with Constant Gain .-120
4.2 Multistep Algorithms.142
4.3 Conclusions . 158
4.4 Exercises.158
4.5 Comments on the Literature.163
5. Sequential Detection; Model Validation 165
5.1 Introduction and Description of the Problem. 166
5.2 Two Elementary Problems and their Solution .171
5.3 Central Limit Theorem and the Asymptotic Local Viewpoint . 176
5.4 Local Methods of Change Detection --.180
5.5 Model Validation by Local Methods . 185
5.6 Conclusion.188
5.7 Annex: Proofs of Theorems 1 and 2 . 188
5.8 Exercises . 191
5.9 Comments on the Literature.197
6. Appendices to Part I 199
6.1 Rudiments of Systems Theory . 199
6.2 Second Order Stationary Processes .205
6.3 Kalman Filters.208
Part II, Stochastic Approximations: Theory 211
1. O.D.E. and Convergence A.S. for an Algorithm with
Locally Bounded Moments 213
LI Introduction of the General Algorithm.213
1.2 Assumptions Peculiar to Chapter 1 . 219
1.3 Decomposition of the General Algorithm.220
1.4 L2 Estimates .223
1.5 Approximation of the Algorithm by the Solution of the O.D.E. . 230
1.6 Asymptotic Analysis of the Algorithm .233
1.7 An Extension of the Previous Results .236
1.8 Alternative Formulation of the Convergence Theorem .238
1.9 A Global Convergence Theorem . 239
1.10 Rate of L2 Convergence of Some Algorithms . 243
1.11 Comments on the Literature .249
Contents
XI
2. Application to the Examples of Part I 251
2Л Geometric Ergodicity of Certain Markov Chains .251
2.2 Markov Chains Dependent on a Parameter в .259
2.3 Linear Dynamical Processes .265
2.4 Examples . 270
2.5 Decision-Feedback Algorithms with Quantisation. 276
2.6 Comments on the Literature.* 288
3. Analysis of the Algorithm in the General Case 289
ЗЛ New Assumptions and Control of the Moments . 289
3.2 Lq Estimates . 293
3.3 Convergence towards the Mean Trajectory . 298
3.4 Asymptotic Analysis of the Algorithm . 301
3.5 “Tube of Confidence” for an Infinite Horizon . 305
3.6 Final Remark. Connections with the Results of Chapter 1 .306
3.7 Comments on the Literature . 306
4. Gaussian Approximations to the Algorithms 307
4.1 Process Distributions and their Weak Convergence . 308
4.2 Diffusions. Gaussian Diffusions .о.,.,,.,,.«. 312
4.3 The Process Uy(t) for an Algorithm with Constant Step Size . 314
4.4 Gaussian Approximation of the Processes i/7(t) . 321.
4.5 Gaussian Approximation for Algorithms with Decreasing
Step Size.327
4.6 Gaussian Approximation and Asymptotic Behaviour
of Algorithms with Constant Steps. 334
4.7 Remark on Weak Convergence Techniques .341
4.8 Comments on the Literature.341
5. Appendix to Part II: A Simple Theorem in the
“Robbins-Monro” Case 343
5.1 The Algorithm, the Assumptions and the Theorem.343
5.2 Proof of the Theorem _._. 344
5.3 Variants . 345
Bibliography
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Subject Index to Part I
Ù 0
m.
Subject Index to Part II
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64 |
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| id | DE-604.BV042635197 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-21T17:00:44Z |
| institution | BVB |
| isbn | 3642758967 9783642758966 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028067694 |
| oclc_num | 914280357 |
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| owner | DE-739 |
| owner_facet | DE-739 |
| physical | XII, 364 S. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer-Verl. |
| record_format | marc |
| series | Stochastic modelling and applied probability |
| series2 | Stochastic modelling and applied probability |
| spelling | Benveniste, Albert Verfasser aut Adaptive algorithms and stochastic approximations Alvert Benveniste ; Michel Metivier ; Pierre Priouret Softcover repr. of the hardcover 1. ed. 1990 Berlin Springer-Verl. [2012] XII, 364 S. txt rdacontent n rdamedia nc rdacarrier Stochastic modelling and applied probability 22 Stochastische Approximation (DE-588)4183371-5 gnd rswk-swf Adaptives System (DE-588)4247928-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Adaptives System (DE-588)4247928-9 s Stochastische Approximation (DE-588)4183371-5 s DE-604 Algorithmus (DE-588)4001183-5 s Métivier, Michel 1931-1988 Verfasser (DE-588)172256585 aut Priouret, Pierre Verfasser aut Stochastic modelling and applied probability 22 (DE-604)BV000895226 22 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028067694&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benveniste, Albert Métivier, Michel 1931-1988 Priouret, Pierre Adaptive algorithms and stochastic approximations Stochastic modelling and applied probability Stochastische Approximation (DE-588)4183371-5 gnd Adaptives System (DE-588)4247928-9 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4183371-5 (DE-588)4247928-9 (DE-588)4001183-5 |
| title | Adaptive algorithms and stochastic approximations |
| title_auth | Adaptive algorithms and stochastic approximations |
| title_exact_search | Adaptive algorithms and stochastic approximations |
| title_full | Adaptive algorithms and stochastic approximations Alvert Benveniste ; Michel Metivier ; Pierre Priouret |
| title_fullStr | Adaptive algorithms and stochastic approximations Alvert Benveniste ; Michel Metivier ; Pierre Priouret |
| title_full_unstemmed | Adaptive algorithms and stochastic approximations Alvert Benveniste ; Michel Metivier ; Pierre Priouret |
| title_short | Adaptive algorithms and stochastic approximations |
| title_sort | adaptive algorithms and stochastic approximations |
| topic | Stochastische Approximation (DE-588)4183371-5 gnd Adaptives System (DE-588)4247928-9 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Stochastische Approximation Adaptives System Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028067694&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
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