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Benveniste, Albert, Metivier, Michel, Priouret, Pierre:

Adaptive Algorithms and Stochastic Approximations (Stochastic Modelling and Applied Probability, 22, Band 22) - Erstausgabe

1990, ISBN: 9783540528944

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Übersetzer: Wilson, S.S. Springer, Gebundene Ausgabe, Auflage: 1, 376 Seiten, Publiziert: 1990-12-05T00:00:01Z, Produktgruppe: Buch, 1.58 kg, Verkaufsrang: 3530279, Informatik, IT-Ausbild… Mehr…

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Benveniste, Albert, Metivier, Michel, Priouret, Pierre:

Adaptive Algorithms and Stochastic Approximations (Stochastic Modelling and Applied Probability, 22, Band 22) - Erstausgabe

1990, ISBN: 9783540528944

Gebundene Ausgabe

Übersetzer: Wilson, S.S. Springer, Gebundene Ausgabe, Auflage: 1, 376 Seiten, Publiziert: 1990-12-05T00:00:01Z, Produktgruppe: Buch, 1.58 kg, Informatik, IT-Ausbildung & -Berufe, Computer… Mehr…

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Benveniste, Albert; Metivier, Michel; Priouret, Pierre:
Adaptive Algorithms and Stochastic Approximations. - gebunden oder broschiert

1990

ISBN: 9783540528944

[PU: Berlin, Heidelberg, New York: Springer-Verlag 1990], With 24 Figures, XI, 365 S., gebundene Ausgabe Applications of Mathematics, Band 22. Zust: Gutes Exemplar., DE, [SC: 3.00], gebra… Mehr…

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Pierre Priouret,Michel Metivier,Albert Benveniste:
Adaptive Algorithms and Stochastic Approximations - gebunden oder broschiert

ISBN: 3540528946

[EAN: 9783540528944], [SC: 0.0], [PU: Springer], Befriedigend/Good: Durchschnittlich erhaltenes Buch bzw. Schutzumschlag mit Gebrauchsspuren, aber vollständigen Seiten. / Describes the av… Mehr…

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Adaptive Algorithms and Stochastic Approximations. - Benveniste, Albert; Metivier, Michel; Priouret, Pierre
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Benveniste, Albert; Metivier, Michel; Priouret, Pierre:
Adaptive Algorithms and Stochastic Approximations. - gebunden oder broschiert

1990, ISBN: 3540528946

[EAN: 9783540528944], [SC: 3.0], [PU: Berlin, Heidelberg, New York: Springer-Verlag], Applications of Mathematics, Band 22. Zust: Gutes Exemplar. With 24 Figures, XI, 365 S., Englisch 712… Mehr…

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Bibliographische Daten des bestpassenden Buches

Details zum Buch
Adaptive Algorithms and Stochastic Approximations (Stochastic Modelling and Applied Probability, 22, Band 22)

Adaptive systems are widely encountered in many applications ranging through adaptive filtering and more generally adaptive signal processing, systems identification and adaptive control, to pattern recognition and machine intelligence: adaptation is now recognised as keystone of intelligence within computerised systems. These diverse areas echo the classes of models which conveniently describe each corresponding system. Thus although there can hardly be a general theory of adaptive systems encompassing both the modelling task and the design of the adaptation procedure, nevertheless, these diverse issues have a major common component: namely the use of adaptive algorithms, also known as stochastic approximations in the mathematical statistics literature, that is to say the adaptation procedure (once all modelling problems have been resolved). The juxtaposition of these two expressions in the title reflects the ambition of the authors to produce a reference work, both for engineers who use these adaptive algorithms and for probabilists or statisticians who would like to study stochastic approximations in terms of problems arising from real applications. Hence the book is organised in two parts, the first one user-oriented, and the second providing the mathematical foundations to support the practice described in the first part. The book covers the topcis of convergence, convergence rate, permanent adaptation and tracking, change detection, and is illustrated by various realistic applications originating from these areas of applications.

Detailangaben zum Buch - Adaptive Algorithms and Stochastic Approximations (Stochastic Modelling and Applied Probability, 22, Band 22)


EAN (ISBN-13): 9783540528944
ISBN (ISBN-10): 3540528946
Gebundene Ausgabe
Erscheinungsjahr: 1990
Herausgeber: Springer

Buch in der Datenbank seit 2007-06-01T20:24:41+02:00 (Berlin)
Detailseite zuletzt geändert am 2024-01-24T22:12:02+01:00 (Berlin)
ISBN/EAN: 3540528946

ISBN - alternative Schreibweisen:
3-540-52894-6, 978-3-540-52894-4
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: benveniste, michel metivier, michel albert, benvéniste, michel pierre
Titel des Buches: approximations, stochastic approximation, algorithms


Daten vom Verlag:

Autor/in: Albert Benveniste; Michel Metivier; Pierre Priouret
Titel: Stochastic Modelling and Applied Probability; Adaptive Algorithms and Stochastic Approximations
Verlag: Springer; Springer Berlin
364 Seiten
Erscheinungsjahr: 1990-12-05
Berlin; Heidelberg; DE
Übersetzer/in: S.S. Wilson (Französisch)
Gewicht: 0,715 kg
Sprache: Englisch
85,55 € (DE)
87,95 € (AT)
106,60 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Wahrscheinlichkeitsrechnung und Statistik; Verstehen; Rang; stochastic approximation; Moment; statistics; System identification; behavior; pattern recognition; Markov chain; Extension; control; cognition; Parameter; ergodicity; modeling; intelligence; A; Probability Theory and Stochastic Processes; Mathematics and Statistics; Math. Applications in Chemistry; Computational Intelligence; Stochastik; Mathematik für Wissenschaftler; Chemie; Künstliche Intelligenz; BC; EA

I. Adaptive Algorithms: Applications.- 1. General Adaptive Algorithm Form.- 1.1 Introduction.- 1.2 Two Basic Examples and Their Variants.- 1.3 General Adaptive Algorithm Form and Main Assumptions.- 1.4 Problems Arising.- 1.5 Summary of the Adaptive Algorithm Form: Assumptions (A).- 1.6 Conclusion.- 1.7 Exercises.- 1.8 Comments on the Literature.- 2. Convergence: the ODE Method.- 2.1 Introduction.- 2.2 Mathematical Tools: Informal Introduction.- 2.3 Guide to the Analysis of Adaptive Algorithms.- 2.4 Guide to Adaptive Algorithm Design.- 2.5 The Transient Regime.- 2.6 Conclusion.- 2.7 Exercises.- 2.8 Comments on the Literature.- 3. Rate of Convergence.- 3.1 Mathematical Tools: Informal Description.- 3.2 Applications to the Design of Adaptive Algorithms with Decreasing Gain.- 3.3 Conclusions from Section 3.2.- 3.4 Exercises.- 3.5 Comments on the Literature.- 4. Tracking Non-Stationary Parameters.- 4.1 Tracking Ability of Algorithms with Constant Gain.- 4.2 Multistep Algorithms.- 4.3 Conclusions.- 4.4 Exercises.- 4.5 Comments on the Literature.- 5. Sequential Detection; Model Validation.- 5.1 Introduction and Description of the Problem.- 5.2 Two Elementary Problems and their Solution.- 5.3 Central Limit Theorem and the Asymptotic Local Viewpoint.- 5.4 Local Methods of Change Detection.- 5.5 Model Validation by Local Methods.- 5.6 Conclusion.- 5.7 Annex: Proofs of Theorems 1 and 2.- 5.8 Exercises.- 5.9 Comments on the Literature.- 6. Appendices to Part I.- 6.1 Rudiments of Systems Theory.- 6.2 Second Order Stationary Processes.- 6.3 Kaiman Filters.- II. Stochastic Approximations: Theory.- 1. O.D.E. and Convergence A.S. for an Algorithm with Locally Bounded Moments.- 1.1 Introduction of the General Algorithm.- 1.2 Assumptions Peculiar to Chapter 1.- 1.3 Decomposition of the General Algorithm.- 1.4 L2 Estimates.- 1.5 Approximation of the Algorithm by the Solution of the O.D.E.- 1.6 Asymptotic Analysis of the Algorithm.- 1.7 An Extension of the Previous Results.- 1.8 Alternative Formulation of the Convergence Theorem.- 1.9 A Global Convergence Theorem.- 1.10 Rate of L2 Convergence of Some Algorithms.- 1.11 Comments on the Literature.- 2. Application to the Examples of Part I.- 2.1 Geometric Ergodicity of Certain Markov Chains.- 2.2 Markov Chains Dependent on a Parameter ?.- 2.3 Linear Dynamical Processes.- 2.4 Examples.- 2.5 Decision-Feedback Algorithms with Quantisation.- 2.6 Comments on the Literature.- 3. Analysis of the Algorithm in the General Case.- 3.1 New Assumptions and Control of the Moments.- 3.2 Lq Estimates.- 3.3 Convergence towards the Mean Trajectory.- 3.4 Asymptotic Analysis of the Algorithm.- 3.5 “Tube of Confidence” for an Infinite Horizon.- 3.6 Final Remark. Connections with the Results of Chapter 1.- 3.7 Comments on the Literature.- 4. Gaussian Approximations to the Algorithms.- 4.1 Process Distributions and their Weak Convergence.- 4.2 Diffusions. Gaussian Diffusions.- 4.3 The Process U?(t) for an Algorithm with Constant Step Size.- 4.4 Gaussian Approximation of the Processes U?(t).- 4.5 Gaussian Approximation for Algorithms with Decreasing Step Size.- 4.6 Gaussian Approximation and Asymptotic Behaviour of Algorithms with Constant Steps.- 4.7 Remark on Weak Convergence Techniques.- 4.8 Comments on the Literature.- 5. Appendix to Part II: A Simple Theorem in the “Robbins-Monro” Case.- 5.1 The Algorithm, the Assumptions and the Theorem.- 5.2 Proof of the Theorem.- 5.3 Variants.- Subject Index to Part I.- Subject Index to Part II.
Adaptation is now recognised as a keystone of "intelligence" within computerised systems. This book is a reference work, both for engineers who use stochastic approximations in terms of problems arising from real applications. Relevant application areas are adaptive filtering and more generally adaptive signal processing, systems identification and adaptive control, and several aspects of pattern recognition and machine intelligence.

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