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Author | : Harold Kushner |
Publisher | : Springer Science & Business Media |
Total Pages | : 436 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1468404415 |
Download Numerical Methods for Stochastic Control Problems in Continuous Time Book in PDF, ePub and Kindle
This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new prob lem formulations and sometimes surprising applications appear regularly. We have chosen forms of the models which cover the great bulk of the for mulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types. Both the "drift" and the "variance" might be controlled. The cost functions might be any of the standard types: Discounted, stopped on first exit from a set, finite time, optimal stopping, average cost per unit time over the infinite time interval, and so forth.
Author | : Harold Kushner |
Publisher | : Springer Science & Business Media |
Total Pages | : 480 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 146130007X |
Download Numerical Methods for Stochastic Control Problems in Continuous Time Book in PDF, ePub and Kindle
Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.
Author | : Harold J. Kushner |
Publisher | : Springer Science & Business Media |
Total Pages | : 496 |
Release | : 2001 |
Genre | : Language Arts & Disciplines |
ISBN | : 9780387951393 |
Download Numerical Methods for Stochastic Control Problems in Continuous Time Book in PDF, ePub and Kindle
The required background is surveyed, and there is an extensive development of methods of approximation and computational algorithms. The book is written on two levels: algorithms and applications, and mathematical proofs. Thus, the ideas should be very accessible to a broad audience."--BOOK JACKET.
Author | : Harold Joseph Kushner |
Publisher | : Springer Science & Business Media |
Total Pages | : 439 |
Release | : 1992 |
Genre | : Distribution (Probability theory) |
ISBN | : 9780387978345 |
Download Numerical Methods for Stochastic Control Problems in Continuous Time Book in PDF, ePub and Kindle
Stochastic control is a very active area of research and this monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels: that of practice (algorithms and applications) and that of mathematical development. It is broadly accessible for graduate students and researchers.
Author | : Harold Kushner |
Publisher | : Springer Science & Business Media |
Total Pages | : 295 |
Release | : 2008-12-19 |
Genre | : Science |
ISBN | : 0817646213 |
Download Numerical Methods for Controlled Stochastic Delay Systems Book in PDF, ePub and Kindle
The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. The book is the first on the subject and will be of great interest to all those who work with stochastic delay equations and whose main interest is either in the use of the algorithms or in the mathematics. An excellent resource for graduate students, researchers, and practitioners, the work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control.
Author | : Wendell H. Fleming |
Publisher | : Springer Science & Business Media |
Total Pages | : 231 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461263808 |
Download Deterministic and Stochastic Optimal Control Book in PDF, ePub and Kindle
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 | : Atle Seierstad |
Publisher | : Springer Science & Business Media |
Total Pages | : 299 |
Release | : 2010-07-03 |
Genre | : Mathematics |
ISBN | : 0387766170 |
Download Stochastic Control in Discrete and Continuous Time Book in PDF, ePub and Kindle
This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1), piecewise - terministic control problems (Chapter 3), and control of Ito diffusions (Chapter 4). The chapters include treatments of optimal stopping problems. An Appendix - calls material from elementary probability theory and gives heuristic explanations of certain more advanced tools in probability theory. The book will hopefully be of interest to students in several ?elds: economics, engineering, operations research, ?nance, business, mathematics. In economics and business administration, graduate students should readily be able to read it, and the mathematical level can be suitable for advanced undergraduates in mathem- ics and science. The prerequisites for reading the book are only a calculus course and a course in elementary probability. (Certain technical comments may demand a slightly better background. ) As this book perhaps (and hopefully) will be read by readers with widely diff- ing backgrounds, some general advice may be useful: Don’t be put off if paragraphs, comments, or remarks contain material of a seemingly more technical nature that you don’t understand. Just skip such material and continue reading, it will surely not be needed in order to understand the main ideas and results. The presentation avoids the use of measure theory.
Author | : Maurizio Falcone |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2019-02-05 |
Genre | : Science |
ISBN | : 9783030019587 |
Download Numerical Methods for Optimal Control Problems Book in PDF, ePub and Kindle
This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.
Author | : Nawaf Bou-Rabee |
Publisher | : American Mathematical Soc. |
Total Pages | : 124 |
Release | : 2019-01-08 |
Genre | : Random walks (Mathematics) |
ISBN | : 1470431815 |
Download Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations Book in PDF, ePub and Kindle
This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates a Markov jump process that can be realized exactly using a Monte Carlo method. In this construction the jump size of the approximation can be bounded uniformly in space, which often guarantees that the schemes are numerically stable for both finite and long time simulation of SDEs.
Author | : Wendell H. Fleming |
Publisher | : Springer Science & Business Media |
Total Pages | : 436 |
Release | : 2006-02-04 |
Genre | : Mathematics |
ISBN | : 0387310711 |
Download Controlled Markov Processes and Viscosity Solutions Book in PDF, ePub and Kindle
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.