Bücher der Reihe Stochastic Modelling and Applied Probability

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.

The basis for this book is a number of lectures given frequently by the author to third year students of the Department of Economics at Leningrad State University who specialize in economical cybernetics.

This monograph develops subjects which could be unified under the title "Stochastic Tikhonov-Levinson theory and its applications." The emphasis is on systems where the fast variables converge uniformly outside the boundary layer. Uniform expansions and large deviations are investigated in detail.

The book deals mainly with three problems involving Gaussian stationary processes. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.

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.

This book is an introduction to optimal stochastic control for continuous time Markov processes and the 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.

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 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.

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.

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.

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

"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....

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 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.

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.

"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 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.

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.

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.

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.

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.

BALAKRISHNAN v Preface to the First Edition The title "Applied Functional Analysis" is intended to be short for "Functional analysis in a Hilbert space and certain of its applications," the applications being drawn mostly from areas variously referred to as system optimization or control systems or systems analysis.

In dealing with problems of applied and numerical mathematics the author sought to focus his attention on those complicated problems of mathe matical physics which, in the course of their solution, can be reduced to simpler and theoretically better developed problems allowing effective algorithmic realization on modern computers.

The object of queueing theory (or the theory of mass service) is the investigation of stochastic processes of a special form which are called queueing (or service) processes in this book.

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.

Following the publication of the Japanese edition of this book, several inter esting developments took place in the area. Speed v Preface The physical phenomenon described by Robert Brown was the complex and erratic motion of grains of pollen suspended in a liquid.

Thus, we have to deal with situations in which the systems are only nearly decomposable in the sense that there are weak links among the irreducible subsystems, which dictate the oc- sional regime changes of the system.