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OverviewThis celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science. Full Product DetailsAuthor: L. C. G. Rogers (University of Bath) , David Williams (University of Bath)Publisher: Cambridge University Press Imprint: Cambridge University Press (Virtual Publishing) Edition: 2nd Revised edition ISBN: 9780511805141ISBN 10: 0511805144 Publication Date: 05 August 2014 Audience: Professional and scholarly , Professional & Vocational Format: Undefined Publisher's Status: Active Availability: In stock We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsSome frequently used notation; 4. Introduction to Ito calculus; 4.1. Some motivating remarks; 4.2. Some fundamental ideas: previsible processes, localization, etc.; 4.3. The elementary theory of finite-variation processes; 4.4. Stochastic integrals: the L2 theory; 4.5. Stochastic integrals with respect to continuous semimartingales; 4.6. Applications of Ito's formula; 5. Stochastic differential equations and diffusions; 5.1. Introduction; 5.2. Pathwise uniqueness, strong SDEs, flows; 5.3. Weak solutions, uniqueness in law; 5.4. Martingale problems, Markov property; 5.5. Overture to stochastic differential geometry; 5.6. One-dimensional SDEs; 5.7. One-dimensional diffusions; 6. The general theory; 6.1. Orientation; 6.2. Debut and section theorems; 6.3. Optional projections and filtering; 6.4. Characterising previsible times; 6.5. Dual previsible projections; 6.6. The Meyer decomposition theorem; 6.7. Stochastic integration: the general case; 6.8. Ito excursion theory; References; Index.Reviews'I welcome the paperback edition version of this masterfully written text.' Paul Embrechts, JASA 'The monograph as a whole is warmly recommended to post-PhD students of probability and will be welcomed as a good and reliable reference.' EMS '... will be read with pleasure and advantage by experts in the field and its applications, as well as by those probabilists and others who wish to learn the subject ... an exciting and enjoyable introduction to the rich ideas of the Ito calculus ... there is nothing dry about this book, for its authors have already breathed life into a vibrant subject.' Mathematics Today 'I welcome the paperback edition version of this masterfully written text.' Paul Embrechts, JASA 'The monograph as a whole is warmly recommended to post-PhD students of probability and will be welcomed as a good and reliable reference.' EMS '… will be read with pleasure and advantage by experts in the field and its applications, as well as by those probabilists and others who wish to learn the subject … an exciting and enjoyable introduction to the rich ideas of the Itô calculus … there is nothing dry about this book, for its authors have already breathed life into a vibrant subject.' Mathematics Today Author InformationTab Content 6Author Website:Countries AvailableAll regions |