## Introduction to Stochastic Dynamic Programming

**Author**: Sheldon M. Ross

**Publisher:**Academic Press

**ISBN:**1483269094

**Category:**Mathematics

**Page:**178

**View:**4407

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Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented. The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.

## Decision theory

*an introduction to dynamic programming and sequential decisions*

**Author**: John Bather

**Publisher:**John Wiley & Sons Inc

**ISBN:**9780471976486

**Category:**Business & Economics

**Page:**191

**View:**2667

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Decision Theory An Introduction to Dynamic Programming and Sequential Decisions John Bather University of Sussex, UK Mathematical induction, and its use in solving optimization problems, is a topic of great interest with many applications. It enables us to study multistage decision problems by proceeding backwards in time, using a method called dynamic programming. All the techniques needed to solve the various problems are explained, and the author's fluent style will leave the reader with an avid interest in the subject. * Tailored to the needs of students of optimization and decision theory * Written in a lucid style with numerous examples and applications * Coverage of deterministic models: maximizing utilities, directed networks, shortest paths, critical path analysis, scheduling and convexity * Coverage of stochastic models: stochastic dynamic programming, optimal stopping problems and other special topics * Coverage of advanced topics: Markov decision processes, minimizing expected costs, policy improvements and problems with unknown statistical parameters * Contains exercises at the end of each chapter, with hints in an appendix Aimed primarily at students of mathematics and statistics, the lucid text will also appeal to engineering and science students and those working in the areas of optimization and operations research.

## Introduction to Dynamic Programming

*International Series in Modern Applied Mathematics and Computer Science*

**Author**: Leon Cooper,Mary W. Cooper

**Publisher:**Elsevier

**ISBN:**1483136620

**Category:**Mathematics

**Page:**300

**View:**8143

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Introduction to Dynamic Programming introduces the reader to dynamic programming and presents the underlying mathematical ideas and results, as well as the application of these ideas to various problem areas. A large number of solved practical problems and computational examples are included to clarify the way dynamic programming is used to solve problems. A consistent notation is applied throughout the text for the expression of quantities such as state variables and decision variables. This monograph consists of 10 chapters and opens with an overview of dynamic programming as a particular approach to optimization, along with the basic components of any mathematical optimization model. The following chapters discuss the application of dynamic programming to variational problems; functional equations and the principle of optimality; reduction of state dimensionality and approximations; and stochastic processes and the calculus of variations. The final chapter looks at several actual applications of dynamic programming to practical problems, such as animal feedlot optimization and optimal scheduling of excess cash investment. This book should be suitable for self-study or for use as a text in a one-semester course on dynamic programming at the senior or first-year, graduate level for students of mathematics, statistics, operations research, economics, business, industrial engineering, or other engineering fields.

## Wahrscheinlichkeitstheorie und Stochastische Prozesse

**Author**: Michael Mürmann

**Publisher:**Springer-Verlag

**ISBN:**364238160X

**Category:**Mathematics

**Page:**428

**View:**4204

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Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.

## Grundbegriffe der Wahrscheinlichkeitstheorie

**Author**: K. Hinderer

**Publisher:**Springer-Verlag

**ISBN:**364280957X

**Category:**Mathematics

**Page:**248

**View:**7919

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## Introduction to the Mathematics of Operations Research with Mathematica®, Second Edition

**Author**: Kevin J. Hastings

**Publisher:**CRC Press

**ISBN:**9781574446128

**Category:**Business & Economics

**Page:**592

**View:**7091

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The breadth of information about operations research and the overwhelming size of previous sources on the subject make it a difficult topic for non-specialists to grasp. Fortunately, Introduction to the Mathematics of Operations Research with Mathematica®, Second Edition delivers a concise analysis that benefits professionals in operations research and related fields in statistics, management, applied mathematics, and finance. The second edition retains the character of the earlier version, while incorporating developments in the sphere of operations research, technology, and mathematics pedagogy. Covering the topics crucial to applied mathematics, it examines graph theory, linear programming, stochastic processes, and dynamic programming. This self-contained text includes an accompanying electronic version and a package of useful commands. The electronic version is in the form of Mathematica notebooks, enabling you to devise, edit, and execute/reexecute commands, increasing your level of comprehension and problem-solving. Mathematica sharpens the impact of this book by allowing you to conveniently carry out graph algorithms, experiment with large powers of adjacency matrices in order to check the path counting theorem and Markov chains, construct feasible regions of linear programming problems, and use the "dictionary" method to solve these problems. You can also create simulators for Markov chains, Poisson processes, and Brownian motions in Mathematica, increasing your understanding of the defining conditions of these processes. Among many other benefits, Mathematica also promotes recursive solutions for problems related to first passage times and absorption probabilities.

## An Introduction to Nonlinear Analysis: Applications

**Author**: Zdzislaw Denkowski,Stanisław Migórski,Nikolaos Socrates Papageorgiou

**Publisher:**Springer Science & Business Media

**ISBN:**9780306474569

**Category:**Mathematics

**Page:**823

**View:**5104

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This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.

## Introduction to Modern Economic Growth

**Author**: Daron Acemoglu

**Publisher:**Princeton University Press

**ISBN:**1400835771

**Category:**Business & Economics

**Page:**1008

**View:**5565

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Introduction to Modern Economic Growth is a groundbreaking text from one of today's leading economists. Daron Acemoglu gives graduate students not only the tools to analyze growth and related macroeconomic problems, but also the broad perspective needed to apply those tools to the big-picture questions of growth and divergence. And he introduces the economic and mathematical foundations of modern growth theory and macroeconomics in a rigorous but easy to follow manner. After covering the necessary background on dynamic general equilibrium and dynamic optimization, the book presents the basic workhorse models of growth and takes students to the frontier areas of growth theory, including models of human capital, endogenous technological change, technology transfer, international trade, economic development, and political economy. The book integrates these theories with data and shows how theoretical approaches can lead to better perspectives on the fundamental causes of economic growth and the wealth of nations. Innovative and authoritative, this book is likely to shape how economic growth is taught and learned for years to come. Introduces all the foundations for understanding economic growth and dynamic macroeconomic analysis Focuses on the big-picture questions of economic growth Provides mathematical foundations Presents dynamic general equilibrium Covers models such as basic Solow, neoclassical growth, and overlapping generations, as well as models of endogenous technology and international linkages Addresses frontier research areas such as international linkages, international trade, political economy, and economic development and structural change An accompanying Student Solutions Manual containing the answers to selected exercises is available (978-0-691-14163-3/$24.95). See: http://press.princeton.edu/titles/8970.html. For Professors only: To access a complete solutions manual online, email us at: [email protected]

## Markov Decision Processes

*Discrete Stochastic Dynamic Programming*

**Author**: Martin L. Puterman

**Publisher:**John Wiley & Sons

**ISBN:**1118625870

**Category:**Mathematics

**Page:**684

**View:**1788

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The Wiley-Interscience Paperback Series consists of selected booksthat have been made more accessible to consumers in an effort toincrease global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "This text is unique in bringing together so many resultshitherto found only in part in other texts and papers. . . . Thetext is fairly self-contained, inclusive of some basic mathematicalresults needed, and provides a rich diet of examples, applications,and exercises. The bibliographical material at the end of eachchapter is excellent, not only from a historical perspective, butbecause it is valuable for researchers in acquiring a goodperspective of the MDP research potential." —Zentralblatt fur Mathematik ". . . it is of great value to advanced-level students,researchers, and professional practitioners of this field to havenow a complete volume (with more than 600 pages) devoted to thistopic. . . . Markov Decision Processes: Discrete Stochastic DynamicProgramming represents an up-to-date, unified, and rigoroustreatment of theoretical and computational aspects of discrete-timeMarkov decision processes." —Journal of the American Statistical Association

## Approximate Dynamic Programming

*Solving the Curses of Dimensionality*

**Author**: Warren B. Powell

**Publisher:**John Wiley & Sons

**ISBN:**9780470182956

**Category:**Mathematics

**Page:**480

**View:**7314

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## An Elementary Introduction to Dynamic Programming

*A State Equation Approach*

**Author**: Brian Gluss

**Publisher:**N.A

**ISBN:**N.A

**Category:**Dynamic programming

**Page:**402

**View:**4422

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## Introduction to Stochastic Programming

**Author**: John R. Birge,François Louveaux

**Publisher:**Springer Science & Business Media

**ISBN:**1461402379

**Category:**Business & Economics

**Page:**485

**View:**3449

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The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. In this extensively updated new edition there is more material on methods and examples including several new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods including approximate dynamic programming, robust optimization and online methods. The book is highly illustrated with chapter summaries and many examples and exercises. Students, researchers and practitioners in operations research and the optimization area will find it particularly of interest. Review of First Edition: "The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make 'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998)

## Vehicle Propulsion Systems

*Introduction to Modeling and Optimization*

**Author**: Lino Guzzella,Antonio Sciarretta

**Publisher:**Springer Science & Business Media

**ISBN:**3540746927

**Category:**Technology & Engineering

**Page:**338

**View:**4840

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The authors of this text have written a comprehensive introduction to the modeling and optimization problems encountered when designing new propulsion systems for passenger cars. It is intended for persons interested in the analysis and optimization of vehicle propulsion systems. Its focus is on the control-oriented mathematical description of the physical processes and on the model-based optimization of the system structure and of the supervisory control algorithms.

## Introduction to Stochastic Programming

**Author**: John Birge,François Louveaux

**Publisher:**Springer Science & Business Media

**ISBN:**9780387982175

**Category:**Mathematics

**Page:**421

**View:**2919

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This rapidly developing field encompasses many disciplines including operations research, mathematics, and probability. Conversely, it is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors present a broad overview of the main themes and methods of the subject, thus helping students develop an intuition for how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. The early chapters introduce some worked examples of stochastic programming, demonstrate how a stochastic model is formally built, develop the properties of stochastic programs and the basic solution techniques used to solve them. The book then goes on to cover approximation and sampling techniques and is rounded off by an in-depth case study. A well-paced and wide-ranging introduction to this subject.

## Stochastic Models, Estimation, and Control

**Author**: Peter S. Maybeck

**Publisher:**Academic Press

**ISBN:**9780080960036

**Category:**Mathematics

**Page:**291

**View:**5202

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This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.

## An introduction to dynamic programming

*the theory of multistage decision processes*

**Author**: O. L. R. Jacobs

**Publisher:**N.A

**ISBN:**N.A

**Category:**Dynamic programming

**Page:**126

**View:**6881

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## Deterministic and Stochastic Optimal Control

**Author**: Wendell H. Fleming,Raymond W. Rishel

**Publisher:**Springer Science & Business Media

**ISBN:**1461263808

**Category:**Mathematics

**Page:**222

**View:**9607

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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.

## Introduction to stochastic control

**Author**: Harold Joseph Kushner

**Publisher:**N.A

**ISBN:**N.A

**Category:**Science

**Page:**390

**View:**7376

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The text treats stochastic control problems for Markov chains, discrete time Markov processes, and diffusion models, and discusses method of putting other problems into the Markovian framework. Computational methods are discussed and compared for Markov chain problems. Other topics include the fixed and free time of control, discounted cost, minimizing the average cost per unit time, and optimal stopping. Filtering and conrol for linear systems, and stochastic stability for discrete time problems are discussed thoroughly. The book gives a detailed treatment of the simpler problems, and fills the need to introduce the student to the more sophisticated mathematical concepts required for advanced theory by describing their roles and necessity in an intuitive and natural way. Diffusion models are developed as limits of stochastic difference equations and also via the stochastic integral approach. Examples and exercises are included. (Author).

## Stochastic Control Theory

*Dynamic Programming Principle*

**Author**: Makiko Nisio

**Publisher:**Springer

**ISBN:**4431551239

**Category:**Mathematics

**Page:**250

**View:**5159

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This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.

## An Introduction to Mathematical Analysis for Economic Theory and Econometrics

**Author**: Dean Corbae,Maxwell B. Stinchcombe,Juraj Zeman

**Publisher:**Princeton University Press

**ISBN:**1400833086

**Category:**Business & Economics

**Page:**688

**View:**5350

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Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory