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The DMV seminar "Stochastische Approximation und Optimierung zufalliger Systeme" was held at Blaubeuren, 28. 5. -4. 6. 1989. The goal was to give an approach to theory and application of stochas tic approximation in view of optimization problems, especially in engineering systems. These notes are based on the seminar lectures. They consist of three parts: I. Foundations of stochastic approximation (H. Walk); n. Applicational aspects of stochastic approximation (G. PHug); In. Applications to adaptation :ugorithms (L. Ljung). The prerequisites for reading this book are basic knowledge in probability, mathematical statistics, optimization. We would like to thank Prof. M. Barner and Prof. G. Fischer for the or ganization of the seminar. We also thank the participants for their cooperation and our assistants and secretaries for typing the manuscript. November 1991 L. Ljung, G. PHug, H. Walk Table of contents I Foundations of stochastic approximation (H. Walk)
1 Almost sure convergence of stochastic approximation procedures 2
2 Recursive methods for linear problems 17
3 Stochastic optimization under stochastic constraints 22
4 A learning model; recursive density estimation 27
5 Invariance principles in stochastic approximation 30
6 On the theory of large deviations 43 References for Part I 45 11 Applicational aspects of stochastic approximation (G. PHug)
7 Markovian stochastic optimization and stochastic approximation procedures 53
8 Asymptotic distributions 71
9 Stopping times 79
1O Applications of stochastic approximation methods 80 References for Part II 90 III Applications to adaptation algorithms (L.
Table des matières
I Foundations of stochastic approximation.-
1 Almost sure convergence of stochastic approximation procedures.-
2 Recursive methods for linear problems.-
3 Stochastic optimization under stochastic constraints.-
4 A learning model; recursive density estimation.-
5 Invariance principles in stochastic approximation.-
6 On the theory of large deviations.- References for Part I.- II Applicational aspects of stochastic approximation.-
7 Markovian stochastic optimization and stochastic approximation procedures.-
8 Asymptotic distributions.-
9 Stopping times.-
10 Applications of stochastic approximation methods.- References for Part II.- III Applications to adaptation algorithms.-
11 Adaptation and tracking.-
12 Algorithm development.-
13 Asymptotic Properties in the decreasing gain case.-
14 Estimation of the tracking ability of the algorithms.- References for Part III.
