Itô calculus

著者

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

書誌事項

Itô calculus

L.C.G. Rogers and David Williams

（Wiley series in probability and mathematical statistics, . Probability and mathematical statistics . Diffusions, Markov processes, and martingales ; v. 2）

Wiley, c1987

注記

Bibliography: p. 449-468

Includes index

内容説明・目次

内容説明

The main themes of this book are stochastic integrals, stochastic differential equations, excursion theory and 'the general theory of processes'. Much effort has gone into the attempt to make these subjects accessible by providing many concrete examples illustrating techniques of calculation, and by treating all topics (including stochastic differential geometry) from the ground up, starting from the simplest case. In particular, the theory is developed first for the 'continuous' case, by far the most important in practice, while the general theory (and its applications) forms the last chapter. Many of the examples and many of the proofs are new and some important methods of calculation appear for the first time in a book. Stochastic differential equations are widely used in practice: in electrical engineering; in controlling systems subject to random 'noise'; in modelling economic systems; and in several branches of physics and chemistry. They are also used to great effect in other branches of mathematics, such as the theory of partial differential equations, differential geometry and complex analysis. Researchers and practitioners in all these fields will find it a useful and highly readable reference work.

目次

• INTRODUCTION TO ITO CALCULUS: Some Motivating Remarks
• Some Fundamental Ideas: Previsible Processes, Localizabtion, 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
• The Debut and Section Theorems
• Optional Projections and Filtering
• Characterizing Previsible Times
• Dual Previsible Projections
• The Meyer Decomposition Theorem
• Stochastic Integration: The General Case
• Excursion Theory.

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詳細情報

• NII書誌ID(NCID): BA01323133
• ISBN:
  • 0471914827
• LCCN: 78016634
• 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: Chichester ; New York
• ページ数/冊数: xiii, 475 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA274.7
  • DC : 519.2/33
  • NDC8 : 417.1
• 件名:
  • LCSH : Markov processes
  • LCSH : Diffusion processes
  • LCSH : Martingales (Mathematics)
• 親書誌ID:
  • BA00019013