LEADER 04365nam 2200805 a 450 001 9910791968603321 005 20200520144314.0 010 $a3-11-025816-1 024 7 $a10.1515/9783110258165 035 $a(CKB)2560000000079418 035 $a(EBL)835465 035 $a(OCoLC)772845223 035 $a(SSID)ssj0000591852 035 $a(PQKBManifestationID)11336347 035 $a(PQKBTitleCode)TC0000591852 035 $a(PQKBWorkID)10727462 035 $a(PQKB)10233833 035 $a(MiAaPQ)EBC835465 035 $a(DE-B1597)124080 035 $a(OCoLC)979584734 035 $a(DE-B1597)9783110258165 035 $a(Au-PeEL)EBL835465 035 $a(CaPaEBR)ebr10527867 035 $a(CaONFJC)MIL628121 035 $a(PPN)175588007 035 $a(EXLCZ)992560000000079418 100 $a20110926d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic models for fractional calculus$b[electronic resource] /$fMark M. Meerschaert, Alla Sikorskii 210 $aBerlin ;$aBoston $cDe Gruyter$dc2012 215 $a1 online resource (304 p.) 225 1 $aDe Gruyter studies in mathematics,$x0179-0986 ;$v43 300 $aDescription based upon print version of record. 311 $a1-306-96870-4 311 $a3-11-025869-2 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tPreface / $rMeerschaert, Mark M. / Sikorskii, Alla -- $tAcknowledgments -- $tContents -- $tChapter 1. Introduction -- $tChapter 2. Fractional Derivatives -- $tChapter 3. Stable Limit Distributions -- $tChapter 4. Continuous Time Random Walks -- $tChapter 5. Computations in R -- $tChapter 6. Vector Fractional Diffusion -- $tChapter 7. Applications and Extensions -- $tBibliography -- $tIndex 330 $aFractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field. 410 0$aDe Gruyter studies in mathematics ;$v43. 606 $aFractional calculus 606 $aDiffusion processes 606 $aStochastic analysis 610 $aAnomalous Diffusion. 610 $aFractional Calculus Model. 610 $aFractional Derivative. 610 $aFractional Diffusion Equation. 610 $aParticle Jump. 610 $aProbability. 610 $aRandom Walk. 610 $aSatistical Physics. 610 $aTempered Fractional Derivative. 610 $aVector Fractional Derivative. 615 0$aFractional calculus. 615 0$aDiffusion processes. 615 0$aStochastic analysis. 676 $a515/.83 686 $aSK 950$2rvk 700 $aMeerschaert$b Mark M.$f1955-$053538 701 $aSikorskii$b Alla$0515174 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910791968603321 996 $aStochastic models for fractional calculus$9856081 997 $aUNINA