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Author : R. L. Stratonovich
Publisher : Unknown
Page : 380 pages
File Size : 51,8 Mb
Release : 1968
Category : Mathematics
ISBN : UOM:39015006052453
Author : Ellida M. Khazen
Publisher : Xlibris Corporation
Page : 320 pages
File Size : 49,5 Mb
Release : 2009-11-16
Category : Education
ISBN : 9781462807178
This book provides the reader with some insight into the mathematical models of random processes with continuous time, stochastic differential equations and stochastic integrals. An advanced development of the mathematical methods of optimal statistical decisions, statistical sequential analysis, and informational estimation of risks, and new methods and solutions to the important problems of the theory of optimal control are presented. The new original results obtained by this author and published shortly in her numerous scientific-research papers are presented in a systematic way in this book. The book is intended for engineers, students, post-graduate students, and scientist researchers. The presentation of the material is accessible to engineers.
Author : William Coffey,Yu. P. Kalmykov,J. T. Waldron
Publisher : World Scientific
Page : 436 pages
File Size : 50,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9810216513
The book is suitable for a lecture course on the theory of Brownian motion, being based on final year undergraduate lectures given at Trinity College, Dublin. Topics that are discussed include: white noise; the Chapman-Kolmogorov equation ? Kramers-Moyal expansion; the Langevin equation; the Fokker-Planck equation; Brownian motion of a free particle; spectral density and the Wiener-Khintchin theorem ? Brownian motion in a potential application to the Josephson effect, ring laser gyro; Brownian motion in two dimensions; harmonic oscillators; itinerant oscillators; linear response theory; rotational Brownian motion; application to loss processes in dielectric and ferrofluids; superparamagnetism and nonlinear relaxation processes.As the first elementary book on the Langevin equation approach to Brownian motion, this volume attempts to fill in all the missing details which students find particularly hard to comprehend from the fundamental papers contained in the Dover reprint ? Selected Papers on Noise and Stochastic Processes, ed. N Wax (1954) ? together with modern applications particularly to relaxation in ferrofluids and polar dielectrics.
Author : Qiying Hu,Wuyi Yue
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 40,8 Mb
Release : 2007-09-14
Category : Business & Economics
ISBN : 9780387369518
Put together by two top researchers in the Far East, this text examines Markov Decision Processes - also called stochastic dynamic programming - and their applications in the optimal control of discrete event systems, optimal replacement, and optimal allocations in sequential online auctions. This dynamic new book offers fresh applications of MDPs in areas such as the control of discrete event systems and the optimal allocations in sequential online auctions.
Author : Wendell H. Fleming,Raymond W. Rishel
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263807
This book may be regarded as consisting of two parts. In Chapters I-IV we pre sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning reader may find it useful first to learn the main results, corollaries, and examples. These tend to be found in the earlier parts of each chapter. We have deliberately postponed some difficult technical proofs to later parts of these chapters. In the second part of the book we give an introduction to stochastic optimal control for Markov diffusion processes. Our treatment follows the dynamic pro gramming method, and depends on the intimate relationship between second order partial differential equations of parabolic type and stochastic differential equations. This relationship is reviewed in Chapter V, which may be read inde pendently of Chapters I-IV. Chapter VI is based to a considerable extent on the authors' work in stochastic control since 1961. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.
Author : Wendell H. Fleming,Halil Mete Soner
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 40,7 Mb
Release : 2006-02-04
Category : Mathematics
ISBN : 9780387310718
This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
Author : A. B. Piunovskiy
Publisher : World Scientific
Page : 308 pages
File Size : 45,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9781848167940
This invaluable book provides approximately eighty examples illustrating the theory of controlled discrete-time Markov processes. Except for applications of the theory to real-life problems like stock exchange, queues, gambling, optimal search etc, the main attention is paid to counter-intuitive, unexpected properties of optimization problems. Such examples illustrate the importance of conditions imposed in the theorems on Markov Decision Processes. Many of the examples are based upon examples published earlier in journal articles or textbooks while several other examples are new. The aim was to collect them together in one reference book which should be considered as a complement to existing monographs on Markov decision processes.The book is self-contained and unified in presentation.The main theoretical statements and constructions are provided, and particular examples can be read independently of others. Examples in Markov Decision Processes is an essential source of reference for mathematicians and all those who apply the optimal control theory to practical purposes. When studying or using mathematical methods, the researcher must understand what can happen if some of the conditions imposed in rigorous theorems are not satisfied. Many examples confirming the importance of such conditions were published in different journal articles which are often difficult to find. This book brings together examples based upon such sources, along with several new ones. In addition, it indicates the areas where Markov decision processes can be used. Active researchers can refer to this book on applicability of mathematical methods and theorems. It is also suitable reading for graduate and research students where they will better understand the theory.
Author : Herman Rubin,Anirban DasGupta
Publisher : IMS
Page : 442 pages
File Size : 49,6 Mb
Release : 2004
Category : Bayesian statistical decision theory
ISBN : 0940600617
Author : A. Bensoussan,J.-L. Lions
Publisher : Elsevier
Page : 563 pages
File Size : 45,8 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 0080875335
Applications of Variational Inequalities in Stochastic Control
Author : Ruslan L. Stratonovich
Publisher : Springer Nature
Page : 419 pages
File Size : 41,5 Mb
Release : 2020-01-14
Category : Mathematics
ISBN : 9783030228330
This English version of Ruslan L. Stratonovich’s Theory of Information (1975) builds on theory and provides methods, techniques, and concepts toward utilizing critical applications. Unifying theories of information, optimization, and statistical physics, the value of information theory has gained recognition in data science, machine learning, and artificial intelligence. With the emergence of a data-driven economy, progress in machine learning, artificial intelligence algorithms, and increased computational resources, the need for comprehending information is essential. This book is even more relevant today than when it was first published in 1975. It extends the classic work of R.L. Stratonovich, one of the original developers of the symmetrized version of stochastic calculus and filtering theory, to name just two topics. Each chapter begins with basic, fundamental ideas, supported by clear examples; the material then advances to great detail and depth. The reader is not required to be familiar with the more difficult and specific material. Rather, the treasure trove of examples of stochastic processes and problems makes this book accessible to a wide readership of researchers, postgraduates, and undergraduate students in mathematics, engineering, physics and computer science who are specializing in information theory, data analysis, or machine learning.
Author : Michiel Hazewinkel,J.C. Williams
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400985469
In the last five years or so there has been an important renaissance in the area of (mathematical) modeling, identification and (stochastic) control. It was the purpose of the Advanced Study Institute of which the present volume constitutes the proceedings to review recent developments in this area with par ticular emphasis on identification and filtering and to do so in such a manner that the material is accessible to a wide variety of both embryo scientists and the various breeds of established researchers to whom identification, filtering, etc. are important (such as control engineers, time series analysts, econometricians, probabilists, mathematical geologists, and various kinds of pure and applied mathematicians; all of these were represented at the ASI). For these proceedings we have taken particular care to see to it that the material presented will be understandable for a quite diverse audience. To that end we have added a fifth tutorial section (besides the four presented at the meeting) and have also included an extensive introduction which explains in detail the main problem areas and themes of these proceedings and which outlines how the various contributions fit together to form a coherent, integrated whole. The prerequisites needed to understand the material in this volume are modest and most graduate students in e. g. mathematical systems theory, applied mathematics, econo metrics or control engineering will qualify.
Author : Alan Bain,Dan Crisan
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 52,8 Mb
Release : 2008-10-08
Category : Mathematics
ISBN : 9780387768960
This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.
Author : Albert N. Shiryaev
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 52,9 Mb
Release : 2007-09-23
Category : Mathematics
ISBN : 9783540740117
Although three decades have passed since the first publication of this book, it is reprinted now as a result of popular demand. The content remains up-to-date and interesting for many researchers as is shown by the many references to it in current publications. The author is one of the leading experts of the field and gives an authoritative treatment of a subject.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,5 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789814518284
Author : R.S. Liptser,A.N. Shiryayev
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 54,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475742930