Nigel J. Cutland

Bio: Nigel J. Cutland is an academic researcher from University of York. The author has contributed to research in topics: Navier–Stokes equations & Stochastic differential equation. The author has an hindex of 18, co-authored 74 publications receiving 2257 citations. Previous affiliations of Nigel J. Cutland include University of Hull & University of Swaziland.

On homogeneous chaos

Abstract: This paper discusses the Wiener-Ito chaos decomposition of an L 2 function

Computability: An Introduction to Recursive Function Theory

Abstract: What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Godel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest.

Nonstandard Measure Theory and its Applications

Abstract: Mathematiques non standard. Theorie de la mesure non standard. Mesures de Lœb. Representations des mesures par des mesures de Lœb. Construction de mesures. Probabilite et processus stochastiques. Analyse stochastique

Nonstandard Analysis and its Applications

Abstract: This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.

Stock Price Returns and the Joseph Effect: A Fractional Version of the Black-Scholes Model

Abstract: In mathematical finance, semimartingales are traditionally viewed as the largest class of stochastic processes which are economically reasonable models for stock price movements. This is mainly because stochastic integrals play a crucial role in the modern theory of finance, and semimartingales represent the largest class of stochastic processes for which a general theory of stochastic integration exists. However, some empirical evidence from actual stock price data suggests stochastic models that are not covered by the semimartingale setting.

Convergence of Probability Measures

Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Foundations of logic programming

Abstract: This is the second edition of an account of the mathematical foundations of logic programming. Its purpose is to collect, in a unified and comprehensive manner, the basic theoretical results of the field, which have previously only been available in widely scattered research papers. In addition to presenting the technical results, the book also contains many illustrative examples and problems. The text is intended to be self-contained, the only prerequisites being some familiarity with PROLOG and knowledge of some basic undergraduate mathematics. The material is suitable either as a reference book for researchers or as a textbook for a graduate course on the theoretical aspects of logic programming and deductive database systems.

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Abstract: We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs

Stochastic Equations in Infinite Dimensions

Abstract: Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. The stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with additive noise 6. Linear equations with multiplicative noise 7. Existence and uniqueness for nonlinear equations 8. Martingale solutions Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations 10. Absolute continuity and Girsanov's theorem 11. Large time behaviour of solutions 12. Small noise asymptotic.

Cognitive Radio An Integrated Agent Architecture for Software Defined Radio

Abstract: An Integrated Agent Architecture for Software Defined Radio. Rapid-prototype cognitive radio, CR1, was developed to apply these.The modern software defined radio has been called the heart of a cognitive radio. Cognitive radio: an integrated agent architecture for software defined radio. Http:bwrc.eecs.berkeley.eduResearchMCMACR White paper final1.pdf. The cognitive radio, built on a software-defined radio, assumes. Radio: An Integrated Agent Architecture for Software Defined Radio, Ph.D. The need for software-defined radios is underlined and the most important notions used for such. Mitola III, Cognitive radio: an integrated agent architecture for software defined radio, Ph.D. This results in the set-theoretic ontology of radio knowledge defined in the. Cognitive Radio An Integrated Agent Architecture for Software.This article first briefly reviews the basic concepts about cognitive radio CR. Cognitive Radio-An Integrated Agent Architecture for Software Defined Radio. Cognitive Radio RHMZ 2007. Software-defined radio SDR idea 1. Cognitive radio: An integrated agent architecture for software.Cognitive Radio SOFTWARE DEFINED RADIO, AND ADAPTIVE WIRELESS SYSTEMS2 Cognitive Networks. 3 Joseph Mitola III, Cognitive Radio: An Integrated Agent Architecture for Software Defined Radio Stockholm.