Stochastic Analysis, Control, Optimization and Applications


Book Description

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.




Stochastic Processes and Filtering Theory


Book Description

This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well. Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.




Stochastic Analysis, Filtering, and Stochastic Optimization


Book Description

This volume is a collection of research works to honor the late Professor Mark H.A. Davis, whose pioneering work in the areas of Stochastic Processes, Filtering, and Stochastic Optimization spans more than five decades. Invited authors include his dissertation advisor, past collaborators, colleagues, mentees, and graduate students of Professor Davis, as well as scholars who have worked in the above areas. Their contributions may expand upon topics in piecewise deterministic processes, pathwise stochastic calculus, martingale methods in stochastic optimization, filtering, mean-field games, time-inconsistency, as well as impulse, singular, risk-sensitive and robust stochastic control.




Advances in Filtering and Optimal Stochastic Control


Book Description

This volume contains contributions to a conference on filtering, optimal stochastic control, and related topics, held in Cocoyoc, Mexico, in February 1982. In addition to specialists in nonlinear filtering and stochastic control, several outstanding probabilists working in related fields were an important element in the conference. The focus was not only on the mathematical aspects of the theory, but on newer areas of application and on numerical techniques of approximate solutions to problems in filtering and stochastic control.




Advances in Control Systems


Book Description

Advances in Control Systems: Theory and Applications, Volume 5 provides information pertinent to the significant progress in the field of control and systems theory and applications. This book presents the problem of the optimal control of a system. Organized into six chapters, this volume begins with an overview of the fundamental conditions in the calculus of variations that are basic to the optimal control problem. This text then examines one of the basic problems in control and systems theory in general. Other chapters consider a number of rather basic results in optimal nonlinear filtering and describe the characteristic function of the state of vector of a nonlinear system. This book discusses as well a significant application area of control and systems theory, which is the optimal control of nuclear reactors. The final chapter deals with optimal control with bounds on the state variables. This book is a valuable resource for practicing engineers.




Advancing Research in Information and Communication Technology


Book Description

For 60 years the International Federation for Information Processing (IFIP) has been advancing research in Information and Communication Technology (ICT). This book looks into both past experiences and future perspectives using the core of IFIP's competence, its Technical Committees (TCs) and Working Groups (WGs). Soon after IFIP was founded, it established TCs and related WGs to foster the exchange and development of the scientific and technical aspects of information processing. IFIP TCs are as diverse as the different aspects of information processing, but they share the following aims: To establish and maintain liaison with national and international organizations with allied interests and to foster cooperative action, collaborative research, and information exchange. To identify subjects and priorities for research, to stimulate theoretical work on fundamental issues, and to foster fundamental research which will underpin future development. To provide a forum for professionals with a view to promoting the study, collection, exchange, and dissemination of ideas, information, and research findings and thereby to promote the state of the art. To seek and use the most effective ways of disseminating information about IFIP’s work including the organization of conferences, workshops and symposia and the timely production of relevant publications. To have special regard for the needs of developing countries and to seek practicable ways of working with them. To encourage communication and to promote interaction between users, practitioners, and researchers. To foster interdisciplinary work and – in particular – to collaborate with other Technical Committees and Working Groups. The 17 contributions in this book describe the scientific, technical, and further work in TCs and WGs and in many cases also assess the future consequences of the work’s results. These contributions explore the developments of IFIP and the ICT profession now and over the next 60 years. The contributions are arranged per TC and conclude with the chapter on the IFIP code of ethics and conduct.




Stochastic Analysis


Book Description

Stochastic Analysis: Liber Amicorum for Moshe Zakai focuses on stochastic differential equations, nonlinear filtering, two-parameter martingales, Wiener space analysis, and related topics. The selection first ponders on conformally invariant and reflection positive random fields in two dimensions; real time architectures for the Zakai equation and applications; and quadratic approximation by linear systems controlled from partial observations. Discussions focus on predicted miss, review of basic sequential detection problems, multigrid algorithms for the Zakai equation, invariant test functions and regularity, and reflection positivity. The text then takes a look at a model of stochastic differential equation in Hubert spaces applicable to Navier Stokes equation in dimension 2; wavelets as attractors of random dynamical systems; and Markov properties for certain random fields. The publication examines the anatomy of a low-noise jump filter, nonlinear filtering with small observation noise, and closed form characteristic functions for certain random variables related to Brownian motion. Topics include derivation of characteristic functions for the examples, proof of the theorem, sequential quadratic variation test, asymptotic optimal filters, mean decision time, and asymptotic optimal filters. The selection is a valuable reference for researchers interested in stochastic analysis.




Risk-Sensitive Optimal Control


Book Description

The two major themes of this book are risk-sensitive control and path-integral or Hamiltonian formulation. It covers risk-sensitive certainty-equivalence principles, the consequent extension of the conventional LQG treatment and the path-integral formulation.




Stochastic Processes, Estimation, and Control


Book Description

The authors provide a comprehensive treatment of stochastic systems from the foundations of probability to stochastic optimal control. The book covers discrete- and continuous-time stochastic dynamic systems leading to the derivation of the Kalman filter, its properties, and its relation to the frequency domain Wiener filter aswell as the dynamic programming derivation of the linear quadratic Gaussian (LQG) and the linear exponential Gaussian (LEG) controllers and their relation to HÝsubscript 2¨ and HÝsubscript Ýinfinity¨¨ controllers and system robustness. This book is suitable for first-year graduate students in electrical, mechanical, chemical, and aerospace engineering specializing in systems and control. Students in computer science, economics, and possibly business will also find it useful.




Stochastic Processes, Finance And Control: A Festschrift In Honor Of Robert J Elliott


Book Description

This book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners. The topics considered will be diverse in applications, and will provide contemporary approaches to the problems considered. The areas considered are rapidly evolving. This volume will contribute to their development, and present the current state-of-the-art stochastic processes, analysis, filtering and control.Contributing authors include: H Albrecher, T Bielecki, F Dufour, M Jeanblanc, I Karatzas, H-H Kuo, A Melnikov, E Platen, G Yin, Q Zhang, C Chiarella, W Fleming, D Madan, R Mamon, J Yan, V Krishnamurthy.