Analysis of Variations for Self-similar Processes A Stochastic Calculus Approach /

• Main Author: Tudor, Ciprian. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2013.
• Series: Probability and Its Applications,
• Subjects: Mathematics.; Distribution (Probability theory).; Statistics.; Probability Theory and Stochastic Processes.; Statistics, general.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-319-00936-0

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 analy...

Table of Contents:

• Preface
• Introduction
• Part I Examples of Self-Similar Processes
• 1.Fractional Brownian Motion and Related Processes
• 2.Solutions to the Linear Stochastic Heat and Wave Equation
• 3.Non Gaussian Self-Similar Processes
• 4.Multiparameter Gaussian Processes
• Part II Variations of Self-Similar Process: Central and Non-Central Limit Theorems
• 5.First and Second Order Quadratic Variations. Wavelet-Type Variations
• 6.Hermite Variations for Self-Similar Processes
• Appendices: A.Self-Similar Processes with Stationary Increments: Basic Properties
• B.Kolmogorov Continuity Theorem
• C.Multiple Wiener Integrals and Malliavin Derivatives
• References
• Index.