Bøger i Stochastic Modelling and Applied Probability serien

Stochastic control theory is a relatively young branch of mathematics. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise.

Focusing on switching diffusion processes that involve both continuous dynamics and discrete events, this comprehensive study moves from basic properties such as Feller and strong Feller to the numerical solutions of switching diffusions and stability.

In wntmg this monograph my aim has been to present a "geometric" approach to the structural synthesis of multivariable control systems that are linear, time-invariant and of finite dynamic order.

Shortly after the end of World War II high-speed digital computing machines were being developed. We discovered, for example, that even Gaus sian elimination was not well understood from a machine point of view and that no effective machine oriented elimination algorithm had been developed.

This book analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail.

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.

This book provides a broad treatment of sampling-based computational methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. General methods and model-specific algorithms are discussed.

This accessible book aims to collect in a single volume the essentials of stochastic networks. Written by leading authors in the field, this book is meant to be used as a reference or supplementary reading by practitioners in operations research, computer systems, communications networks, production planning, and logistics.

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.

This book on mathematical, statistical and stochastic models in reliability will help analysts formulate general failure models, establish formulae for computing performance measures, and determine how to identify optimal replacement policies.

Beginning with Jackson networks and ending with spatial queuing systems, this book describes several basic stochastic network processes, with the focus on network processes that have tractable expressions for the equilibrium probability distribution of the numbers of units at the stations.

Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market.

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations.

"This book is concerned with a probabilistic approach for image analysis, mostly from the Bayesian point of view, and the important Markov chain Monte Carlo methods commonly used....This book will be useful, especially to researchers with a strong background in probability and an interest in image analysis.

This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics.

As more applications are found, interest in Hidden Markov Models continues to grow.

This book articulates a new theory that shows that hierarchical decision making can in fact lead to a near optimization of system goals. The material in the book cuts across disciplines. It will appeal to graduate students and researchers in applied mathematics, operations management, operations research, and system and control theory.

Although three decades have passed since the first publication of this book, it is reprinted now as a result of popular demand. The author is one of the leading experts of the field and gives an authoritative treatment of a subject.

"This book is a highly recommendable survey of mathematical tools and results in applied probability with special emphasis on queueing theory....The second edition at hand is a thoroughly updated and considerably expended version of the first edition....

Using a singular perturbation approach, this book offers a systematic treatment of systems that naturally arise in queuing theory, control and optimisation and manufacturing. Provides a single source for concepts previously scattered throughout the literature.

A self-contained and coherent account of probabilistic techniques, covering: distance measures, kernel rules, nearest neighbour rules, Vapnik-Chervonenkis theory, parametric classification, and feature extraction. Both research workers and graduate students will benefit from this wide-ranging and up-to-date account of a fast- moving field.

This text provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations and martingale duality methods.

This thoroughly revised second edition includes a brand new chapter devoted to volatility risk. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.

The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences.The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations.

Presenting the mathematical foundations of the theory of stationary queuing systems, the Palm theory and the Loynes theory, this extensively revised second edition adds substantial material - mainly exercises and their solutions - to a classic reference.

In insurance and finance applications, questions involving extremal events play an important role. This book sets out to bridge the gap between existing theory and practical applications both from a probabilistic as well as statistical point of view.

From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not."

This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods.