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: This book shows how techniques from the perturbation theory of operators, applied to a quasi-compact positive kernel, may be used to obtain limit theorems for Markov chains or to describe stochastic properties of dynamical systems.A general framework for this method is given and then applied to treat several specific cases. An essential element of this work is the description of the peripheral spectra of a quasi-compact Markov kernel and of its Fourier-Laplace perturbations. This is first done in the ergodic but non-mixing case. This work is extended by the second author to the non-ergodic case.The only prerequisites for this book are a knowledge of the basic techniques of probability theory and of notions of elementary functional analysis.
Описание: The purpose of this book is to provide a careful and accessible account along modern lines of the subject which the title deals, as well as to discuss problems of current interest in the field. More precisely this book is devoted to the functional-analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators which includes as particular cases the Dirichlet and Robin problems. This class of boundary value problems provides a new example of analytic semigroups. As an application, we construct a strong Markov process corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it dies at the time when it reaches the set where the particle is definitely absorbed.
Автор: Cools Название: Monte Carlo and Quasi-Monte Carlo Methods ISBN: 3319335057 ISBN-13(EAN): 9783319335056 Издательство: Springer Рейтинг: Цена: 13584 р. Наличие на складе: Есть у поставщика Поставка под заказ.
This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.
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.
Описание: In this book, the functional inequalities are introduced to describe: (i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap; (ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density; (iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.
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.
Автор: R. Daniel Mauldin Название: Graph Directed Markov Systems ISBN: 0521825385 ISBN-13(EAN): 9780521825382 Издательство: Cambridge Academ Рейтинг: Цена: 9433 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students.
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: 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.
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