Analysis of variations for self-similar processes a stochastic calculus approach Ciprian Tudor

Format:

Book

Author/Creator:

Tudor, Ciprian, 1973- author.

Series:

Probability and its applications (Springer-Verlag) 1431-7028

Probability and Its Applications 1431-7028

Language:

English

Subjects (All):

Self-similar processes.

Calculus of variations.

Distribution (Probability theory).

distribution (statistics-related concept).

Physical Description:

1 online resource

Place of Publication:

Cham Springer 2013

Language Note:

English

System Details:

text file

PDF

Summary:

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 interrrelationship. 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

Contents:

Part I: Examples of Self-similar Processes. Fractional Brownian Motion and Related Processes Solutions to the Linear Stochastic Heat and Wave Equation Non-Gaussian Self-similar Processes Multiparameter Gaussian Processes

Part II: Variations of Self-similar Processes: Central and Non-Central Limit Theorems. First and Second Order Quadratic Variations. Wavelet-Type Variations Hermite Variations for Self-similar Processes

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed August 20, 2013)

Other Format:

Print version:

ISBN:

9783319009360

3319009362

9781299857636

1299857639

3319009354

9783319009353

OCLC:

857431888

Access Restriction:

Restricted for use by site license