Vai al contenuto principale della pagina

Stochastic models for fractional calculus [[electronic resource] /] / Mark M. Meerschaert, Alla Sikorskii



(Visualizza in formato marc)    (Visualizza in BIBFRAME)

Autore: Meerschaert Mark M. <1955-> Visualizza persona
Titolo: Stochastic models for fractional calculus [[electronic resource] /] / Mark M. Meerschaert, Alla Sikorskii Visualizza cluster
Pubblicazione: Berlin ; ; Boston, : De Gruyter, c2012
Descrizione fisica: 1 online resource (304 p.)
Disciplina: 515/.83
Soggetto topico: Fractional calculus
Diffusion processes
Stochastic analysis
Soggetto non controllato: Anomalous Diffusion
Fractional Calculus Model
Fractional Derivative
Fractional Diffusion Equation
Particle Jump
Probability
Random Walk
Satistical Physics
Tempered Fractional Derivative
Vector Fractional Derivative
Classificazione: SK 950
Altri autori: SikorskiiAlla  
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: 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
Sommario/riassunto: 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.
Titolo autorizzato: Stochastic models for fractional calculus  Visualizza cluster
ISBN: 3-11-025816-1
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910791968603321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: De Gruyter studies in mathematics ; ; 43.