The Fourth Pannonian Symposium on Mathematical Statistics was held in Bad Tatzmannsdorf, Austria, 4-10 September, 1983. The first two Symposia were held there in 1979 and 1981; whereas the Third Symposium was staged in Visegrad, Hungary in 1982. The proceedings volumes of these conferences, published by Springer, D. Reidel, and D. Reidel & Akademiai Kiad6, respec tively give information about the objectives of the Pannonian Symposia and the topics covered. About 130 participants from 17 countries took part in this Fourth Symposium, and 92 lectures were presented. This volume contains 21 reviewed contributions which cover various aspects of the application of mathematical statistics. A second group of papers dealing with problems of probability theory and decision theory is published in a separate volume entitled "Probability and Statistidal Decision Theory." Roughly speaking, the papers can be grouped into three main categories. The first group is the application of probability theory. A special type of application is shown in the invited paper of P. Erdos, namely probabilistic methods in number theory. Further models of applied probability covered by the papers are game theory, urn models, best choice models and random graphs. The second group could be best characterized by the term mathematical statistics for models of real data. Such models are linear models, regression, discrimination, time series, analysis of censored data, goodness of fit approxima tion of processes. The papers show the increasing importance of VII new theoretical results (i. e."

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."