UID:
almahu_9949462113402882
Format:
1 online resource (291 p.)
ISBN:
9783110258165
,
9783110494938
Series Statement:
De Gruyter Studies in Mathematics , 43
Content:
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.
Note:
Frontmatter --
,
Preface --
,
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
,
Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DG Studies in Mathematics eBook-Package, De Gruyter, 9783110494938
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011, De Gruyter, 9783110261189
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011, De Gruyter, 9783110261233
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011, De Gruyter, 9783110261202
Additional Edition:
ISBN 9783110258691
Language:
English
Subjects:
Mathematics
DOI:
10.1515/9783110258165
URL:
https://doi.org/10.1515/9783110258165
URL:
https://www.degruyter.com/isbn/9783110258165
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