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This title in other formats:Other titles in the Diffusions, Markov Processes & Martingales series:Diffusions, Markov Processes & Martingales #02: Diffusions, Markov Processes and Martingales: Volume 2, Ito Calculusby L. C. G. Rogers
Synopses & ReviewsPublisher Comments: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. Synopsis:Now available in paperback for the first time; essential reading for all students of probability theory. Synopsis:Desgined for all students of probability theory. Synopsis:Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. This volume follows on from the first, covering 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. 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. 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.
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