Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus: Cambridge Mathematical Library
Autor L. C. G. Rogers, David Williamsen Limba Engleză Paperback – 6 sep 2000
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Specificații
ISBN-13: 9780521775939
ISBN-10: 0521775930
Pagini: 496
Ilustrații: illustrations, bibliography, index
Dimensiuni: 152 x 226 x 23 mm
Greutate: 0.82 kg
Ediția:Revizuită
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Mathematical Library
Locul publicării:Cambridge, United Kingdom
ISBN-10: 0521775930
Pagini: 496
Ilustrații: illustrations, bibliography, index
Dimensiuni: 152 x 226 x 23 mm
Greutate: 0.82 kg
Ediția:Revizuită
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Mathematical Library
Locul publicării:Cambridge, United Kingdom
Cuprins
Some 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.
Recenzii
'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
'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
Descriere
This celebrated volume gives an accessible introduction to stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes.