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Author : Emmanuel Fernández-Gaucherand
Publisher :
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.:/5 (267 download)
Download or read book Controlled Markov processes on the infinite planning horizon written by Emmanuel Fernández-Gaucherand and published by . This book was released on 1991 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : E. Fernández-Gaucherand
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (897 download)
Download or read book Controlled Markov Processes on the Infinite Planning Horizon: Weighted and Overtaking Cost Criteria written by E. Fernández-Gaucherand and published by . This book was released on 1993 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bruce L. Miller
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (227 download)
Download or read book Finite Stage Continuous Time Markov Decision Processes with an Infinite Planning Horizon written by Bruce L. Miller and published by . This book was released on 1967 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: The system considered may be in one of n states at any point in time; its probability law is a Markov process that depends on the policy (control) chosen. The return to the system over a given planning horizon is the integral over that horizon of a return rate that depends on both the policy and the sample path of the process. The objective is to find a policy that maximizes the expected discounted return as the planning horizon tends to infinity. The case where the discount factor goes to zero is also considered. In all cases it is shown that there is a stationary policy that is optimal, and an algorithm is given to obtain that policy. (Author).
Author : Bruce L Miller
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (155 download)
Download or read book Finite State Continuous Time Markov Decision Processes with an Infinite Planning Horizon written by Bruce L Miller and published by . This book was released on 1967 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Onesimo Hernandez-Lerma
Publisher : Springer Science & Business Media
ISBN 13 : 1461207290
Total Pages : 223 pages
Book Rating : 4.4/5 (612 download)
Download or read book Discrete-Time Markov Control Processes written by Onesimo Hernandez-Lerma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the first part of a planned two-volume series devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes (MCPs). Interest is mainly confined to MCPs with Borel state and control (or action) spaces, and possibly unbounded costs and noncompact control constraint sets. MCPs are a class of stochastic control problems, also known as Markov decision processes, controlled Markov processes, or stochastic dynamic pro grams; sometimes, particularly when the state space is a countable set, they are also called Markov decision (or controlled Markov) chains. Regardless of the name used, MCPs appear in many fields, for example, engineering, economics, operations research, statistics, renewable and nonrenewable re source management, (control of) epidemics, etc. However, most of the lit erature (say, at least 90%) is concentrated on MCPs for which (a) the state space is a countable set, and/or (b) the costs-per-stage are bounded, and/or (c) the control constraint sets are compact. But curiously enough, the most widely used control model in engineering and economics--namely the LQ (Linear system/Quadratic cost) model-satisfies none of these conditions. Moreover, when dealing with "partially observable" systems) a standard approach is to transform them into equivalent "completely observable" sys tems in a larger state space (in fact, a space of probability measures), which is uncountable even if the original state process is finite-valued.
Author : Zhenting Hou
Publisher : Springer Science & Business Media
ISBN 13 : 146130265X
Total Pages : 501 pages
Book Rating : 4.4/5 (613 download)
Download or read book Markov Processes and Controlled Markov Chains written by Zhenting Hou and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South American and Asian scholars.
Author : Evgeniĭ Borisovich Dynkin
Publisher : Springer
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.3/5 (91 download)
Download or read book Controlled Markov Processes written by Evgeniĭ Borisovich Dynkin and published by Springer. This book was released on 1979 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the systematic exposition of the contemporary theory of controlled Markov processes with discrete time parameter or in another termi nology multistage Markovian decision processes. We discuss the applications of this theory to various concrete problems. Particular attention is paid to mathe matical models of economic planning, taking account of stochastic factors. The authors strove to construct the exposition in such a way that a reader interested in the applications can get through the book with a minimal mathe matical apparatus. On the other hand, a mathematician will find, in the appropriate chapters, a rigorous theory of general control models, based on advanced measure theory, analytic set theory, measurable selection theorems, and so forth. We have abstained from the manner of presentation of many mathematical monographs, in which one presents immediately the most general situation and only then discusses simpler special cases and examples. Wishing to separate out difficulties, we introduce new concepts and ideas in the simplest setting, where they already begin to work. Thus, before considering control problems on an infinite time interval, we investigate in detail the case of the finite interval. Here we first study in detail models with finite state and action spaces-a case not requiring a departure from the realm of elementary mathematics, and at the same time illustrating the most important principles of the theory.
Author : Tomas Prieto-Rumeau
Publisher : World Scientific
ISBN 13 : 1848168497
Total Pages : 292 pages
Book Rating : 4.8/5 (481 download)
Download or read book Selected Topics on Continuous-time Controlled Markov Chains and Markov Games written by Tomas Prieto-Rumeau and published by World Scientific. This book was released on 2012 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns continuous-time controlled Markov chains, also known as continuous-time Markov decision processes. They form a class of stochastic control problems in which a single decision-maker wishes to optimize a given objective function. This book is also concerned with Markov games, where two decision-makers (or players) try to optimize their own objective function. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science, among other areas. An extensive, self-contained, up-to-date analysis of basic optimality criteria (such as discounted and average reward), and advanced optimality criteria (e.g., bias, overtaking, sensitive discount, and Blackwell optimality) is presented. A particular emphasis is made on the application of the results herein: algorithmic and computational issues are discussed, and applications to population models and epidemic processes are shown. This book is addressed to students and researchers in the fields of stochastic control and stochastic games. Moreover, it could be of interest also to undergraduate and beginning graduate students because the reader is not supposed to have a high mathematical background: a working knowledge of calculus, linear algebra, probability, and continuous-time Markov chains should suffice to understand the contents of the book.
Author : A. B. Piunovskiy
Publisher : World Scientific
ISBN 13 : 1848167938
Total Pages : 308 pages
Book Rating : 4.8/5 (481 download)
Download or read book Examples in Markov Decision Processes written by A. B. Piunovskiy and published by World Scientific. This book was released on 2013 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bruce Leonard Miller
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (227 download)
Download or read book Finite State Continuous Time Markov Decision Processes with a Finite Planning Horizon written by Bruce Leonard Miller and published by . This book was released on 1967 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: The system considered may be in one of n states at any point in time and its probability law is a Markov process which depends on the policy (control) chosen. The return to the system over a given planning horizon is the integral (over that horizon) of a return rate which depends on both the policy and the sample path of the process. The objective is to find a policy which maximizes the expected return over the given planning horizon. A necessary and sufficient condition for optimality is obtained, and a constructive proof is given that there is a piecewise constant policy which is optimal. A bound on the number of switches (points where the piecewise constant policy jumps) is obtained for the case where there are two states. (Author).
Author : Onesimo Hernandez-Lerma
Publisher : Springer Science & Business Media
ISBN 13 : 1461205611
Total Pages : 286 pages
Book Rating : 4.4/5 (612 download)
Download or read book Further Topics on Discrete-Time Markov Control Processes written by Onesimo Hernandez-Lerma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes, the text is mainly confined to MCPs with Borel state and control spaces. Although the book follows on from the author's earlier work, an important feature of this volume is that it is self-contained and can thus be read independently of the first. The control model studied is sufficiently general to include virtually all the usual discrete-time stochastic control models that appear in applications to engineering, economics, mathematical population processes, operations research, and management science.
Author : Xi-Ren Cao
Publisher : Springer Nature
ISBN 13 : 3030418464
Total Pages : 376 pages
Book Rating : 4.0/5 (34 download)
Download or read book Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems written by Xi-Ren Cao and published by Springer Nature. This book was released on 2020-05-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming. The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization. Among the more important novel considerations presented are: the extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and development of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.
Author : Bruce L. Miller
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (663 download)
Download or read book Finite State Continuous Time Markov Processes with a Finite Planning Horizon written by Bruce L. Miller and published by . This book was released on 1967 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniel Hernández-Hernández
Publisher : Springer Science & Business Media
ISBN 13 : 0817683372
Total Pages : 331 pages
Book Rating : 4.8/5 (176 download)
Download or read book Optimization, Control, and Applications of Stochastic Systems written by Daniel Hernández-Hernández and published by Springer Science & Business Media. This book was released on 2012-08-15 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.
Author : Bharat T. Doshi
Publisher :
ISBN 13 :
Total Pages : 492 pages
Book Rating : 4.E/5 ( download)
Download or read book Continuous Time Control of Markov Processes on an Arbitrary State Space written by Bharat T. Doshi and published by . This book was released on 1974 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies the problem of the control of Markov processes with continuous time parameter and arbitrary state space. The economic criteria used are (a) the expected discounted return over an infinite horizon and (b) the expected average return over an infinite horizon. An extensive theory is available to treat the control problems in which either the time parameter or the state space is discrete. This dissertation extends the available theory to the general case of continuous time parameter and arbitrary state space. An application to the control of the arrival process in an M/G/1 queue is included. (Modified author abstract).
Author : Tomás Prieto-Rumeau
Publisher : World Scientific
ISBN 13 : 1848168489
Total Pages : 292 pages
Book Rating : 4.8/5 (481 download)
Download or read book Selected Topics on Continuous-time Controlled Markov Chains and Markov Games written by Tomás Prieto-Rumeau and published by World Scientific. This book was released on 2012 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns continuous-time controlled Markov chains, also known as continuous-time Markov decision processes. They form a class of stochastic control problems in which a single decision-maker wishes to optimize a given objective function. This book is also concerned with Markov games, where two decision-makers (or players) try to optimize their own objective function. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science, among other areas.An extensive, self-contained, up-to-date analysis of basic optimality criteria (such as discounted and average reward), and advanced optimality criteria (e.g., bias, overtaking, sensitive discount, and Blackwell optimality) is presented. A particular emphasis is made on the application of the results herein: algorithmic and computational issues are discussed, and applications to population models and epidemic processes are shown.This book is addressed to students and researchers in the fields of stochastic control and stochastic games. Moreover, it could be of interest also to undergraduate and beginning graduate students because the reader is not supposed to have a high mathematical background: a working knowledge of calculus, linear algebra, probability, and continuous-time Markov chains should suffice to understand the contents of the book.
Author : Eugene A. Feinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1461508053
Total Pages : 560 pages
Book Rating : 4.4/5 (615 download)
Download or read book Handbook of Markov Decision Processes written by Eugene A. Feinberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eugene A. Feinberg Adam Shwartz This volume deals with the theory of Markov Decision Processes (MDPs) and their applications. Each chapter was written by a leading expert in the re spective area. The papers cover major research areas and methodologies, and discuss open questions and future research directions. The papers can be read independently, with the basic notation and concepts ofSection 1.2. Most chap ters should be accessible by graduate or advanced undergraduate students in fields of operations research, electrical engineering, and computer science. 1.1 AN OVERVIEW OF MARKOV DECISION PROCESSES The theory of Markov Decision Processes-also known under several other names including sequential stochastic optimization, discrete-time stochastic control, and stochastic dynamic programming-studiessequential optimization ofdiscrete time stochastic systems. The basic object is a discrete-time stochas tic system whose transition mechanism can be controlled over time. Each control policy defines the stochastic process and values of objective functions associated with this process. The goal is to select a "good" control policy. In real life, decisions that humans and computers make on all levels usually have two types ofimpacts: (i) they cost orsavetime, money, or other resources, or they bring revenues, as well as (ii) they have an impact on the future, by influencing the dynamics. In many situations, decisions with the largest immediate profit may not be good in view offuture events. MDPs model this paradigm and provide results on the structure and existence of good policies and on methods for their calculation.
