Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus

by David Williams, L. C. G. Rogers

September 18, 2000 | Trade Paperback |

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The second volume concentrates on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. These subjects are made accessible in the many concrete examples that illustrate techniques of calculation, and in the treatment of all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appear for the first time in this book.

Format: Trade Paperback

Dimensions: 493 Pages, 5.91 × 8.66 × 0.79 in

Published: September 18, 2000

Language: English

The following ISBNs are associated with this title:

ISBN - 10: 0521775930

ISBN - 13: 9780521775939

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Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus

Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus

by David Williams, L. C. G. Rogers

Format: Trade Paperback

Dimensions: 493 Pages, 5.91 × 8.66 × 0.79 in

Published: September 18, 2000

Language: English

The following ISBNs are associated with this title:

ISBN - 10: 0521775930

ISBN - 13: 9780521775939

Table of Contents

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.

From the Publisher

The second volume concentrates on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. These subjects are made accessible in the many concrete examples that illustrate techniques of calculation, and in the treatment of all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appear for the first time in this book.

Editorial Reviews

''... 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
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