Peter Whittle - Böcker

This classic text, now in its third edition, has been widely used as an introduction to probability. Its main aim is to present a straightforward introduction to the main concepts and applications of probability at an undergraduate level. Historically, the early analysts of games of chance found the question 'What is the fair price for entering this game?' as natural a question as 'What is the probability of winning it?'. This book differs from many textbooks in that the author takes as the starting point for the subject's development expectation rather than the traditional probability measure approach. All the main concepts of a first course in probability are covered including probability measures, independence, conditional probability, the basic limit theorems, and Markov processes. Throughout, the author stresses the importance of applications and includes numerous examples covering a range of difficulties. Little is required in the way of prerequisites - a basic exposure to calculus and matrix algebra will be sufficient for any student to enjoy this first course in probability.

The third edition of 1992 constituted a major reworking of the original text, and the preface to that edition still represents my position on the issues that stimulated me first to write.

The concept of a system as an entity in its own right has emergedwith increasing force in the past few decades in, for example, theareas of electrical and control engineering, economics, ecology,urban structures, automaton theory, operational research andindustry. The more definite concept of a large-scale system isimplicit in these applications, but is particularly evident infields such as the study of communication networks, computernetworks and neural networks. The Wiley-Interscience Series inSystems and Optimization has been established to serve the needs ofresearchers in these rapidly developing fields. It is intended forworks concerned with developments in quantitative systems theory,applications of such theory in areas of interest, or associatedmethodology. This is the first book-length treatment of risk-sensitive control,with many new results. The quadratic cost function of the standardLQG (linear/quadratic/Gaussian) treatment is replaced by theexponential of a quadratic, giving the so-called LEQG formulationallowing for a degree of optimism or pessimism on the part of theoptimiser. The author is the first to achieve formulation and proofof risk-sensitive versions of the certainty-equivalence andseparation principles. Further analysis allows one to formulate theoptimization as the extremization of a path integral and tocharacterize the solution in terms of canonical factorization. Itis thus possible to achieve the long-sought goal of an operationalstochastic maximum principle, valid for a higher-order model, andin fact only evident when the models are extended to therisk-sensitive class. Additional results include deduction ofcompact relations between value functions and canonical factors,the exploitation of the equivalence between policy improvement andNewton Raphson methods and the direct relation of LEQG methods tothe H??? and minimum-entropy methods. This book will proveessential reading for all graduate students, researchers andpractitioners who have an interest in control theory includingmathematicians, engineers, economists, physicists andpsychologists. 1990 Stochastic Programming Peter Kall, Universityof Zurich, Switzerland and Stein W. Wallace, University ofTrondheim, Norway Stochastic Programming is the first textbook toprovide a thorough and self-contained introduction to the subject.Carefully written to cover all necessary background material fromboth linear and non-linear programming, as well as probabilitytheory, the book draws together the methods and techniquespreviously described in disparate sources. After introducing theterms and modelling issues when randomness is introduced in adeterministic mathematical programming model, the authors coverdecision trees and dynamic programming, recourse problems,probabilistic constraints, preprocessing and network problems.Exercises are provided at the end of each chapter. Throughout, theemphasis is on the appropriate use of the techniques, rather thanon the underlying mathematical proofs and theories, making the bookideal for researchers and students in mathematical programming andoperations research who wish to develop their skills in stochasticprogramming. 1994

Point-to-point vs hub-and-spoke. Questions of network design are real and involve many billions of dollars. Yet little is known about optimising design - nearly all work concerns optimising flow assuming a given design. This foundational book tackles optimisation of network structure itself, deriving comprehensible and realistic design principles. With fixed material cost rates, a natural class of models implies the optimality of direct source-destination connections, but considerations of variable load and environmental intrusion then enforce trunking in the optimal design, producing an arterial or hierarchical net. Its determination requires a continuum formulation, which can however be simplified once a discrete structure begins to emerge. Connections are made with the masterly work of Bendsøe and Sigmund on optimal mechanical structures and also with neural, processing and communication networks, including those of the Internet and the World Wide Web. Technical appendices are provided on random graphs and polymer models and on the Klimov index.

Prediction and Regulation by Linear Least-Square Methods was first published in 1963. This revised second edition was issued in 1983. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.During the past two decades, statistical theories of prediction and control have assumed an increasing importance in all fields of scientific research. To understand a phenomenon is to be able to predict it and to influence it in predictable ways. First published in 1963 and long out of print, Prediction and Regulation by Linear Least-Square Methods offers important tools for constructing models of dynamic phenomena. This elegantly written book has been a basic reference for researchers in many applied sciences who seek practical information about the representation and manipulation of stationary stochastic processes. Peter Whittle's text has a devoted group of readers and users, especially among economists. This edition contains the unchanged text of the original and adds new works by the author and a foreword by economist Thomas J. Sargent.

Point-to-point vs hub-and-spoke. Questions of network design are real and involve many billions of dollars. Yet little is known about optimising design - nearly all work concerns optimising flow assuming a given design. This foundational book tackles optimisation of network structure itself, deriving comprehensible and realistic design principles. With fixed material cost rates, a natural class of models implies the optimality of direct source-destination connections, but considerations of variable load and environmental intrusion then enforce trunking in the optimal design, producing an arterial or hierarchical net. Its determination requires a continuum formulation, which can however be simplified once a discrete structure begins to emerge. Connections are made with the masterly work of Bendsøe and Sigmund on optimal mechanical structures and also with neural, processing and communication networks, including those of the Internet and the World Wide Web. Technical appendices are provided on random graphs and polymer models and on the Klimov index.

The third edition of 1992 constituted a major reworking of the original text, and the preface to that edition still represents my position on the issues that stimulated me first to write. The present edition contains a number of minor modifications and corrections, but its principal innovation is the addition of material on dynamic programming, optimal allocation, option pricing and large deviations. These are substantial topics, but ones into which one can gain an insight with less labour than is generally thought. They all involve the expectation concept in an essential fashion, even the treatment of option pricing, which seems initially to forswear expectation in favour of an arbitrage criterion. I am grateful to readers and to Springer-Verlag for their continuing interest in the approach taken in this work. Peter Whittle Preface to the Third Edition This book is a complete revision of the earlier work Probability which appeared in 1970. While revised so radically and incorporatingso much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability, demanding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level' . In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character.