Analysis of Variations for Self-similar Processes
Analysis of Variations for Self-similar Processes
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DOI：
10.1007/978-3-319-00936-0
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
C. Tudor
中科院分区：
文献类型：
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作者：
C. Tudor
自相似过程是一类在适当的时间尺度下分布不变的随机过程，是近几十年来研究的热点。这本书介绍了这些过程的基本性质，并侧重于研究他们的变化使用随机分析。虽然自相似过程，特别是分数布朗运动，已经在几本书中讨论过，但最近在科学文献中出现了一些新的类别。其中一些是分数布朗运动的推广（双分数布朗运动，减布朗运动，Hermite过程），而另一些则是分数噪声驱动的偏微分方程的解.在这本专着中，作者讨论了这些新的自相似过程类的基本性质及其相互关系。与此同时，一种新的方法（基于随机微积分，特别是Malliavin演算）研究的自相似过程的变化的行为已经在过去的十年中发展起来。这项工作调查这些最新的技术和极限定理和Malliavin演算的发现。
Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.