Probability and Its Applications

A Stochastic Calculus Approach

By: Ciprian Tudor

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Paperback | 14 August 2015

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284 Pages

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23.5 x 15.5 x 1.52

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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.

Industry Reviews

"The author provides the general theory for different classes of self-similar processes with a complete treatment of limit theorems for their variations. ... The book is self-contained and suitable for both graduate students with a basic background in probability theory and stochastic processes and researchers whose aim is investigating this topic." (Anthony R©veillac, Mathematical Reviews, February, 2015)

"This monograph is a profound survey of recent developments in the fields of ... self-similar processes and their calculus of variations. ... It may serve as an excellent basis for research seminars or special classes on Gaussian processes and Malliavin's calculus and as a starting point for applied mathematicians with interest in self-similar processes." (Michael H¶gele, zbMATH 1308.60004, 2015)

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