Описание: This second edition of G. Winkler's successful book on random field approaches to image analysis, related Markov Chain Monte Carlo methods, and statistical inference with emphasis on Bayesian image analysis concentrates more on general principles and models and less on details of concrete applications. Addressed to students and scientists from mathematics, statistics, physics, engineering, and computer science, it will serve as an introduction to the mathematical aspects rather than a survey. Basically no prior knowledge of mathematics or statistics is required.The second edition is in many parts completely rewritten and improved, and most figures are new. The topics of exact sampling and global optimization of likelihood functions have been added. This second edition comes with a CD-ROM by F. Friedrich,containing a host of (live) illustrations for each chapter. In an interactive environment, readers can perform their own experiments to consolidate the subject.
Описание: The theory of Markov Decision Processes - also known under several other names including sequential stochastic optimization, discrete-time stochastic control, and stochastic dynamic programming - studies sequential optimization of discrete time stochastic systems. Fundamentally, this is a methodology that examines and analyzes a discrete-time stochastic 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. Its objective is to select a "good" control policy. In real life, decisions that humans and computers make on all levels usually have two types of impacts: (i) they cost or save time, 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 of future events. Markov Decision Processes (MDPs) model this paradigm and provide results on the structure and existence of good policies and on methods for their calculations. MDPs are attractive to many researchers because they are important both from the practical and the intellectual points of view. MDPs provide tools for the solution of important real-life problems. In particular, many business and engineering applications use MDP models. Analysis of various problems arising in MDPs leads to a large variety of interesting mathematical and computational problems. Accordingly, the Handbook of Markov Decision Processes is split into three parts: Part I deals with models with finite state and action spaces and Part II deals with infinite state problems, and Part III examines specific applications. Individual chapters are written by leading experts on the subject.
Автор: Kemeny Название: Denumerable Markov Chains ISBN: 0387901779 ISBN-13(EAN): 9780387901770 Издательство: Springer Цена: 6578 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Presents a systematic treatment of denumerable Markov chains, covering both the foundations of the subject and some in topics in potential theory and boundary theory. This textbook discusses relations among what might be called the descriptive quantities associated with Markov chains-probabilities of events and means of random variables.
Описание: Based on a lecture course given at Chalmers University of Technology, this book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.
Описание: This book presents applications of semi-Markov processes in finance, insurance and reliability, using real-life problems as examples. After a presentation of the main probabilistic tools necessary for understanding of the book, the authors show how to apply semi-Markov processes in finance, starting from the axiomatic definition and continuing eventually to the most advanced financial tools, particularly in insurance and in risk-and-ruin theories. Also considered are reliability problems that interact with credit risk theory in finance. The unique approach of this book is to solve finance and insurance problems with semi-Markov models in a complete way and furthermore present real-life applications of semi-Markov processes.
Описание: Markov decision processes (MDPs), also called stochastic dynamic programming, were first studied in the 1960s. MDPs can be used to model and solve dynamic decision-making problems that are multiperiod and in stochastic circumstances. There are three basic branches in MDPs: discrete-time MDPs, continuous-time MDPs and semi-Markov decision processes. Starting from these three branches, many generalized MDPs models have been applied to various practical problems. These models include partially observable MDPs, adaptive MDPs, MDPs in stochastic environments, and MDPs with multiple objectives, constraints or imprecise parameters. MDPs have been applied in many areas, such as communications, signal processing, artificial intelligence, stochastic scheduling and manufacturing systems, discrete event systems, management and economies.This book examines MDPs and their applications in the optimal control of discrete event systems (DESs), optimal replacement, and optimal allocations in sequential online auctions. The book presents three main topics: вЂў a new methodology for MDPs with discounted total reward criterion; вЂў transformation of continuous-time MDPs and semi-Markov decision processes into a discrete-time MDPs model, thereby simplifying the application of MDPs; вЂў application of MDPs in stochastic environments, which greatly extends the area where MDPs can be applied.Each topic is used to study optimal control problems or other types of problems.
Описание: A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.
Описание: This is a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel` boundary conditions in probability theory. It presents new developments in the theory of singular integrals.
Автор: Costa O.L.V., Fragoso M.D., Marques R.P. Название: Discrete-Time Markov Jump Linear Systems ISBN: 1852337613 ISBN-13(EAN): 9781852337612 Издательство: Springer Рейтинг: Цена: 14629 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Safety critical and high-integrity systems, such as industrial plants and economic systems can be subject to abrupt changes - for instance due to component or interconnection failure, and sudden environment changes etc. Combining probability and operator theory, Discrete-Time Markov Jump Linear Systems provides a unified and rigorous treatment of recent results for the control theory of discrete jump linear systems, which are used in these areas of application. The book is designed for experts in linear systems with Markov jump parameters, but is also of interest for specialists in stochastic control since it presents stochastic control problems for which an explicit solution is possible - making the book suitable for course use. From the reviews:"This text is very well written...it may prove valuable to those who work in the area, are at home with its mathematics, and are interested in stability of linear systems, optimal control, and filtering." Journal of the American Statistical Association, December 2005
Автор: Niederreiter Harald, Talay Denis Название: Monte Carlo and Quasi-Monte Carlo Methods 2004 ISBN: 3540255419 ISBN-13(EAN): 9783540255413 Издательство: Springer Рейтинг: Цена: 19854 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book represents the refereed proceedings of the Sixth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing and of the Second International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations. These conferences were held jointly at Juan-les-Pins (France) in June 2004. The proceedings include carefully selected papers on many aspects of Monte Carlo methods, quasi-Monte Carlo methods, and the numerical solution of partial differential equations. The reader will be informed about current research in these very active areas.
Описание: Surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. This book covers basic principles, as well as various methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo.
Описание: This book represents the refereed proceedings of the Fifth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the National University of Singapore in the year 2002. An important feature are invited surveys of the state of the art in key areas such as multidimensional numerical integration, low-discrepancy point sets, computational complexity, finance, and other applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings also include carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active area.
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