Stochastic Methods

Markov chains are an important idea, related to random walks, which crops up widely in applied stochastic analysis. They are used, for example, in performance modelling and evaluation of computer networks, queuing networks, and telecommunication systems. The main point of the present book is to provide methods, based on the construction of Lyapunov functions, of determining when a Markov chain is ergodic, null recurrent, or transient. These methods can also be extended to the study of questions of stability. Of particular concern are reflected random walks and reflected Brownian motion. The authors provide not only a self-contained introduction to the theory but also details of how the required Lyapunov functions are constructed in various situations.

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who

The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and non-space-clamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.

This 1987 book is a self-contained text on the probabilistic modelling method. It provides the reader with an understanding of the available results as well as with examples of their application. The only background assumed is a knowledge of basic calculus. The necessary fundamentals of probability are presented followed by an introduction to stochastic processes. The remainder of the book is devoted to the treatment of various single-station and their application to uni-programmed and multi-programmed systems and local and wide-area networks. Both exact and approximate solution methods are discussed, with as much emphasis on explaining the ideas and providing information, as on derivations and proofs. This book will still be of use for anyone with an interest in the history of computer science.

Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and method

This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the cont

This comprehensive, handbook style survey of diffusion in condensed matter gives detailed insight in diffusion as the process of particle transport due to stochastic movement which is understood and p

Modern business cycle theory and growth theory uses stochastic dynamic general equilibrium models. In order to solve these models, economists need to use many mathematical tools. This book presents va

This book covers recent advances in efficiency evaluations, most notably Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) methods. It introduces the underlying theories, shows h

Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and method