Diffusions, Markov Processes and Martingales

Volume 2, Ito Calculus

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Paperback | 15 November 2000 | Edition Number 2

At a Glance

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496 Pages

Edition Type
Revised

Dimensions(cm)
22.86 x 15.24 x 2.54

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This 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.

Industry 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

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Some frequently used notation
Introduction to Ito calculus
Some motivating remarks
Some fundamental ideas: previsible processes, localization, etc
The elementary theory of finite-variation processes
Stochastic integrals: the L2 theory
Stochastic integrals with respect to continuous semimartingales
Applications of Ito's formula
Stochastic differential equations and diffusions
Introduction
Pathwise uniqueness, strong SDEs, flows
Weak solutions, uniqueness in law
Martingale problems, Markov property
Overture to stochastic differential geometry
One-dimensional SDEs
One-dimensional diffusions
The general theory
Orientation
Debut and section theorems
Optional projections and filtering
Characterising previsible times
Dual previsible projections
The Meyer decomposition theorem
Stochastic integration; the general case
Ito excursion theory
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Diffusions, Markov Processes and Martingales

Volume 2, Ito Calculus

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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