Stochastic Models for Fractional Calculus

Name: Stochastic Models for Fractional Calculus
Brand: Atlantic Books
SKU: 9783110559071
Price: 17971.0 INR
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by Mark M. Meerschaert , Alla Sikorskii

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ISBN13: 9783110559071
Binding: Hardcover
Subject: N/A
Publisher: de Gruyter
Publisher Imprint: de Gruyter
Publication Date: October 21, 2019
Pages: 337
Original Price: GBP 141.5
Language: English
Edition: Rev. and Ext.
Item Weight: 545 grams
BISAC Subject(s): Probability & Statistics / Stochastic Processes

About The Book

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.

About The Author

Mark M. Meerschaert, Alla Sikorskii, Mohsen Zayernouri, Michigan State University, USA.

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