Stochastic models for fractional calculus / Mark M. Meerschaert, Alla Sikorskii.

Format:

Book

Author/Creator:

Meerschaert, Mark M., 1955-

Contributor:

Sikorskii, Alla.

Series:

De Gruyter studies in mathematics ; 43.

De Gruyter studies in mathematics, 0179-0986 ; 43

Language:

English

Subjects (All):

Fractional calculus.

Diffusion processes.

Stochastic analysis.

Physical Description:

1 online resource (304 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, c2012.

Language Note:

English

Summary:

Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field.

Contents:

Frontmatter

Preface / Meerschaert, Mark M. / Sikorskii, Alla

Acknowledgments

Contents

Chapter 1. Introduction

Chapter 2. Fractional Derivatives

Chapter 3. Stable Limit Distributions

Chapter 4. Continuous Time Random Walks

Chapter 5. Computations in R

Chapter 6. Vector Fractional Diffusion

Chapter 7. Applications and Extensions

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9783110258165

3110258161

OCLC:

772845223