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Meerschaert, Mark M. / Sikorskii, Alla / Zayernouri, Mohsen

Stochastic and Computational Models for Fractional Calculus

Series:De Gruyter Studies in Mathematics

    129,95 € / $149.99 / £118.00*

    Hardcover
    2nd rev. and ext.
    Publication Date:
    2019
    To be published:
    December 2020
    ISBN
    978-3-11-055907-1
    See all formats and pricing

    Overview

    • Develops the theory of fractional calculus and anomalous diffusion using probability theory.
    • Revised and updated edition with a new chapter on numerical methods, including examples and computer codes.
    • With applications in many applied contexts.

    Aims and Scope

    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.

    Details

    24.0 x 17.0 cm
    Approx. xii, 450 pages
    90 Fig.
    Language:
    English
    Type of Publication:
    Monograph
    Keyword(s):

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