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| 本书是第2版(全英文版)。第1版本的《随机积分和微分方程》问世13年以来,有关这方面的书不断涌现,特别是在数学金融方面具有很强应用性的书更是发展迅速。然而没有一本书是真正用函数解析法来表达半鞅和随机积分,这使得新的方法并没有得到很好的应用。尽管这本书不再适合称其为一种新的方法。然而新版本的及时出现,在很大程度上完善了原版本。 |
| Introduction 1 Preliminaries 1 Basic Definitions and Notation 2 Martingales 3 The Poisson Process and Brownian Motion 4 Levv Processes 5 Why the Usual Hypotheses? 6 Local Martingales 7 Stieltjes Integration and Change of Variables 8 Naive Stochastic Integration is Impossible Bibliographic Notes Exercises for Chapter 1 2 Semimartingales and Stochastic Integrals 1 Introduction to Semimartingales 2 Stability Properties of Semimartingales 3 Elementary Examples of Semimartingales 4 Stochastic Integrals 5 Properties of Stochastic Integrals 6 The Quadratic Variation of a Semimartingale 7 Ito's Formula (Change of Variables) 8 Applications of Ito's Formula Bibliographic Notes Exercises for Chapter 2 3 Semimartingales and Decomposable Processes 1 Introduction 2 The Classification of Stopping Times 3 The Doob-Meyer Decompositions 4 Quasimartingales 5 Compensators 6 The Fundamental Theorem of |
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