Itô calculus

著者

• Rogers, L. C. G.
• Williams, D. (David)

書誌事項

Itô calculus

L.C.G. Rogers and David Williams

（Cambridge mathematical library, . Diffusions, Markov processes, and martingales ; v. 2）

Cambridge University Press, 2000

2nd ed

• : pbk

注記

References: p. 449-468

Includes Index to v. 1 and v. 2

First published 1979 and 2nd edition published 1994 by Wiley

Title of "v. 1 : foundations": Diffusions, Markov processes, and martingales (BA46783249)

内容説明・目次

内容説明

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.

目次

• 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.

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詳細情報

• NII書誌ID(NCID): BA48189089
• ISBN:
  • 9780521775939
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: xiii, 480 p.
• 大きさ: 23 cm
• 親書誌ID:
  • BA0151012X