The Malliavin Calculus and Related Topics
The Malliavin Calculus and Related Topics
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DOI：
10.1007/978-1-4757-2437-0
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发表时间：
1995-05
影响因子：
4
通讯作者：
D. Nualart
中科院分区：
文献类型：
--
作者：
D. Nualart
这本书的起源在于邀请给一系列讲座Malliavin演算在概率研讨会的委内瑞拉，在1985年4月。这些讲座的内容在[245]中以西班牙语出版。后来，这些说明完成和改进的两个课程Malliavin演算给予在加州大学欧文分校于1986年和在联邦理工学院德洛桑于1989年。这些课程的内容与本书第1章和第2章中介绍的内容相对应。第3章涉及预期随机微积分，它是从我们与摩西Zakai和Etienne Pardoux合作开发的。1989年7月，在智利圣地亚哥举行的第八届智利概率与统计冬季学校举行的一系列讲座，使我们得以编写一份关于预测演算的教学方法，这是第3章的基础。第四章讨论了Wiener测度的非线性变换及其在研究随机微分方程边值问题解的马氏性中的应用。本章的介绍是受到1992年7月在奥斯陆举行的第四次随机分析研讨会上的演讲的启发。我借此机会感谢这些机构的盛情款待，尤其要感谢恩里克·卡巴纳、马里奥·瓦谢博尔、华金·奥尔特加、苏莱曼·于斯蒂内尔、伯恩特·比尔森达尔、伦佐·凯罗利、勒内·卡莫纳和罗兰多·雷博莱多邀请我就这些主题发表演讲。我们假设读者对伊藤随机微积分和鞅理论有一定的了解。第1.1节。3介绍了伊藤演算，但我们建议读者完成经典伊藤演算的概述，回顾任何优秀的介绍，
The origin of this book lies in an invitation to give a series of lectures on Malliavin calculus at the Probability Seminar of Venezuela, in April 1985. The contents of these lectures were published in Spanish in [245]. Later these notes were completed and improved in two courses on Malliavin calculus given at the University of California at Irvine in 1986 and at École Polytechnique Fédérale de Lausanne in 1989. The contents of these courses correspond to the material presented in Chapters 1 and 2 of this book. Chapter 3 deals with the anticipating stochastic calculus and it was developed from our collaboration with Moshe Zakai and Etienne Pardoux. The series of lectures given at the Eighth Chilean Winter School in Probability and Statistics, at Santiago de Chile, in July 1989, allowed us to write a pedagogical approach to the anticipating calculus which is the basis of Chapter 3. Chapter 4 deals with the nonlinear transformations of the Wiener measure and their applications to the study of the Markov property for solutions to stochastic differential equations with boundary conditions. The presentation of this chapter was inspired by the lectures given at the Fourth Workshop on Stochastic Analysis in Oslo, in July 1992. I take the opportunity to thank these institutions for their hospitality, and in particular I would like to thank Enrique Cabana, Mario Wschebor, Joaquın Ortega, Süleyman Üstünel, Bernt Øksendal, Renzo Cairoli, René Carmona, and Rolando Rebolledo for their invitations to lecture on these topics. We assume that the reader has some familiarity with the Itô stochastic calculus and martingale theory. In Section 1.1. 3 an introduction to the Itô calculus is provided, but we suggest the reader complete this outline of the classical Itô calculus with a review of any of the excellent presentations of