04362nam 2200817 a 450 991081204700332120240516102100.03-11-025816-110.1515/9783110258165(CKB)2560000000079418(EBL)835465(OCoLC)772845223(SSID)ssj0000591852(PQKBManifestationID)11336347(PQKBTitleCode)TC0000591852(PQKBWorkID)10727462(PQKB)10233833(MiAaPQ)EBC835465(DE-B1597)124080(OCoLC)979584734(DE-B1597)9783110258165(Au-PeEL)EBL835465(CaPaEBR)ebr10527867(CaONFJC)MIL628121(PPN)175588007(EXLCZ)99256000000007941820110926d2012 uy 0engur|n|---|||||txtccrStochastic models for fractional calculus /Mark M. Meerschaert, Alla Sikorskii1st ed.Berlin ;Boston De Gruyterc20121 online resource (304 p.)De Gruyter studies in mathematics,0179-0986 ;43Description based upon print version of record.1-306-96870-4 3-11-025869-2 Includes bibliographical references and index. 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 -- IndexFractional 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. De Gruyter studies in mathematics ;43.Fractional calculusDiffusion processesStochastic analysisAnomalous Diffusion.Fractional Calculus Model.Fractional Derivative.Fractional Diffusion Equation.Particle Jump.Probability.Random Walk.Satistical Physics.Tempered Fractional Derivative.Vector Fractional Derivative.Fractional calculus.Diffusion processes.Stochastic analysis.515/.83SK 950rvkMeerschaert Mark M.1955-53538Sikorskii Alla515174MiAaPQMiAaPQMiAaPQBOOK9910812047003321Stochastic models for fractional calculus856081UNINA