G. George Yin - Böcker

The book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. There is a complete development of both probability one and weak convergence methods for very general noise processes. The proofs of convergence use the ODE method, the most powerful to date, with which the asymptotic behavior is characterized by the limit behavior of a mean ODE. The assumptions and proof methods are designed to cover the needs of recent applications. The development proceeds from simple to complex problems, allowing the underlying ideas to be more easily understood. Rate of convergence, iterate averaging, high-dimensional problems, stability-ODE methods, two time scale, asynchronous and decentralized algorithms, general correlated and state-dependent noise, perturbed test function methods, and large devitations methods, are covered. Many motivational examples from learning theory, ergodic cost problems for discrete event systems, wireless communications, adaptive control, signal processing, and elsewhere, illustrate the application of the theory.This second edition is a thorough revision, although the main features and the structure remain unchanged. It contains many additional applications and results, and more detailed discussion. Harold J. Kushner is a University Professor and Professor of Applied Mathematics at Brown University. He has written numerous books and articles on virtually all aspects of stochastic systems theory, and has received various awards including the IEEE Control Systems Field Award.

This edited volume contains 16 research articles. It presents recent and pressing issues in stochastic processes, control theory, differential games, optimization, and their applications in finance, manufacturing, queueing networks, and climate control. One of the salient features is that the book is highly multi-disciplinary. The book is dedicated to Professor Suresh Sethi on the occasion of his 60th birthday, in view of his distinguished career.

This IMA Volume in Mathematics and its Applications Wireless Communications contains papers based on invited lectures at the very successful IMA Sum­ mer Program on Wireless Communications, held on June 22 - July 1, 2005. We would like to thank Prathima Agrawal (Auburn University), Daniel Matthew Andrews (Lucent Technologies), Philip J. Fleming (Mo­ torola, Inc.), George Yin (Wayne State University), and Lisa Zhang (Lucent Technologies) for their superb role as workshop organizers and editors of the proceedings. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Arnd Scheel, Deputy Director of the IMA v PREFACE This volume presents papers, based on invited talks given at the 2005 IMA Summer Workshop on Wireless Communications, held at the Institute for Mathematics and Its Applications, University of Minnesota, June 22 ­ July 1, 2005. The conference provided a well blended program to facilitate the com­ munications between academia and the industry, and to bridge the mathe­ matical sciences, engineering, information theory, and communication com­ munities. The emphases were on design and analysis of computationally efficient algorithms to better understand the behavior and to control the wireless telecommunication networks. As an achieve, this volume presents some of the highlights of the conference, and collects papers covering a broad spectrum of topics. All papers have been reviewed.

This IMA Volume in Mathematics and its Applications TOPICS IN STOCHASTIC ANALYSIS AND NONPARAMETRIC ESTIMATION contains papers that were presented at the IMA Participating Institution conference on "Asymptotic Analysis in Stochastic Processes, Nonparamet­ ric Estimation, and Related Problems" held on September 15-17, 2006 at Wayne State University. The conference, which was one of approximately ten selected each year for partial support by the IMA through its affiliates program, was dedicated to Professor Rafail Z. Khasminskii on the occasion th of his 75 birthday, in recognition of his profound contributions to the field of stochastic processes and nonparametric estimation theory. We are grateful to the participants and, especially, to the conference organizers, for making the event so successful. Pao-Liu Chow, Boris Mor­ dukhovich, and George Yin of the Department of Mathematics at Wayne State University did a superb job organizing this first-rate event and in editing these proceedings. We take this opportunity to thank the Nation al Science Foundation for its support of the IMA.

In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi­ ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza­ tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti­ mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.

This book concerns the identi?cation of systems in which only quantized output observations are available, due to sensor limitations, signal quan- zation, or coding for communications. Although there are many excellent treaties in system identi?cation and its related subject areas, a syst- atic study of identi?cation with quantized data is still in its early stage. This book presents new methodologies that utilize quantized information in system identi?cation and explores their potential in extending control capabilities for systems with limited sensor information or networked s- tems. The book is an outgrowth of our recent research on quantized iden- ?cation; it o?ers several salient features. From the viewpoint of targeted plants, it treats both linear and nonlinear systems, and both time-invariant and time-varying systems. In terms of noise types, it includes independent and dependent noises, stochastic disturbances and deterministic bounded noises, and noises with unknown distribution functions. The key meth- ologies of the book combine empirical measures and information-theoretic approaches to cover convergence, convergence rate, estimator e?ciency, - put design, threshold selection, and complexity analysis. We hope that it can shed new insights and perspectives for system identi?cation.

takes n+1 n n n n its values in some Euclidean space, Y is a random variable, and the “step n size” > 0 is small and might go to zero as n??.

This book focuses on the theory and applications of discrete-time two-time-scale Markov chains. Much effort in this book is devoted to designing system models arising from these applications, analyzing them via analytic and probabilistic techniques, and developing feasible computational algorithms so as to reduce the inherent complexity. This book presents results including asymptotic expansions of probability vectors, structural properties of occupation measures, exponential bounds, aggregation and decomposition and associated limit processes, and interface of discrete-time and continuous-time systems. One of the salient features is that it contains a diverse range of applications on filtering, estimation, control, optimization, and Markov decision processes, and financial engineering. This book will be an important reference for researchers in the areas of applied probability, control theory, operations research, as well as for practitioners who use optimization techniques. Part of the book can also be used in a graduate course of applied probability, stochastic processes, and applications.

This IMA Volume in Mathematics and its Applications TOPICS IN STOCHASTIC ANALYSIS AND NONPARAMETRIC ESTIMATION contains papers that were presented at the IMA Participating Institution conference on "Asymptotic Analysis in Stochastic Processes, Nonparamet­ ric Estimation, and Related Problems" held on September 15-17, 2006 at Wayne State University. The conference, which was one of approximately ten selected each year for partial support by the IMA through its affiliates program, was dedicated to Professor Rafail Z. Khasminskii on the occasion th of his 75 birthday, in recognition of his profound contributions to the field of stochastic processes and nonparametric estimation theory. We are grateful to the participants and, especially, to the conference organizers, for making the event so successful. Pao-Liu Chow, Boris Mor­ dukhovich, and George Yin of the Department of Mathematics at Wayne State University did a superb job organizing this first-rate event and in editing these proceedings. We take this opportunity to thank the Nation al Science Foundation for its support of the IMA.

This edited volume contains 16 research articles. It presents recent and pressing issues in stochastic processes, control theory, differential games, optimization, and their applications in finance, manufacturing, queueing networks, and climate control. One of the salient features is that the book is highly multi-disciplinary. The book is dedicated to Professor Suresh Sethi on the occasion of his 60th birthday, in view of his distinguished career.

In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi­ ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza­ tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti­ mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.

This book encompasses the study of hybrid switching di usion processes and their applications. The word \hybrid" signi es the coexistence of c- tinuous dynamics and discrete events, which is one of the distinct features of the processes under consideration. Much of the book is concerned with the interactions of the continuous dynamics and the discrete events. Our motivations for studying such processes originate from emerging and - isting applications in wireless communications, signal processing, queueing networks, production planning, biological systems, ecosystems, nancial engineering, and modeling, analysis, and control and optimization of lar- scale systems, under the in uence of random environments. Displaying mixture distributions, switching di usions may be described by the associated operators or by systems of stochastic di erential eq- tions together with the probability transition laws of the switching actions. We either have Markov-modulated switching di usions or processes with continuous state-dependent switching. The latter turns out to be much more challenging to deal with. Viewing the hybrid di usions as a number of di usions joined together by the switching process, they may be se- ingly not much di erent from their di usion counterpart. Nevertheless, the underlying problems become more di cult to handle, especially when the switching processes depend on continuous states. The di culty is due to the interaction of the discrete and continuous processes and the tangled and hybrid information pattern.

This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering.

This IMA Volume in Mathematics and its Applications Wireless Communications contains papers based on invited lectures at the very successful IMA Sum­ mer Program on Wireless Communications, held on June 22 - July 1, 2005. We would like to thank Prathima Agrawal (Auburn University), Daniel Matthew Andrews (Lucent Technologies), Philip J. Fleming (Mo­ torola, Inc.), George Yin (Wayne State University), and Lisa Zhang (Lucent Technologies) for their superb role as workshop organizers and editors of the proceedings. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Arnd Scheel, Deputy Director of the IMA v PREFACE This volume presents papers, based on invited talks given at the 2005 IMA Summer Workshop on Wireless Communications, held at the Institute for Mathematics and Its Applications, University of Minnesota, June 22 ­ July 1, 2005. The conference provided a well blended program to facilitate the com­ munications between academia and the industry, and to bridge the mathe­ matical sciences, engineering, information theory, and communication com­ munities. The emphases were on design and analysis of computationally efficient algorithms to better understand the behavior and to control the wireless telecommunication networks. As an achieve, this volume presents some of the highlights of the conference, and collects papers covering a broad spectrum of topics. All papers have been reviewed.