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作者 Meerschaert, Mark M
書名 Stochastic Models for Fractional Calculus
出版項 Berlin/Boston : De Gruyter, Inc., 2011
國際標準書號 9783110258165 (electronic bk.)
book jacket
說明 1 online resource (291 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 De Gruyter Studies in Mathematics Ser. ; v.43
De Gruyter Studies in Mathematics Ser
附註 Intro -- Preface -- Acknowledgments -- 1 Introduction -- 1.1 The traditional diffusion model -- 1.2 Fractional diffusion -- 2 Fractional Derivatives -- 2.1 The Grünwald formula -- 2.2 More fractional derivatives -- 2.3 The Caputo derivative -- 2.4 Time-fractional diffusion -- 3 Stable Limit Distributions -- 3.1 Infinitely divisible laws -- 3.2 Stable characteristic functions -- 3.3 Semigroups -- 3.4 Poisson approximation -- 3.5 Shifted Poisson approximation -- 3.6 Triangular arrays -- 3.7 One-sided stable limits -- 3.8 Two-sided stable limits -- 4 Continuous Time Random Walks -- 4.1 Regular variation -- 4.2 Stable Central Limit Theorem -- 4.3 Continuous time random walks -- 4.4 Convergence in Skorokhod space -- 4.5 CTRW governing equations -- 5 Computations in R -- 5.1 R codes for fractional diffusion -- 5.2 Sample path simulations -- 6 Vector Fractional Diffusion -- 6.1 Vector random walks -- 6.2 Vector random walks with heavy tails -- 6.3 Triangular arrays of random vectors -- 6.4 Stable random vectors -- 6.5 Vector fractional diffusion equation -- 6.6 Operator stable laws -- 6.7 Operator regular variation -- 6.8 Generalized domains of attraction -- 7 Applications and Extensions -- 7.1 LePage Series Representation -- 7.2 Tempered stable laws -- 7.3 Tempered fractional derivatives -- 7.4 Pearson Diffusions -- 7.5 Fractional Pearson diffusions -- 7.6 Fractional Brownian motion -- 7.7 Fractional random fields -- 7.8 Applications of fractional diffusion -- 7.9 Applications of vector fractional diffusion -- Bibliography -- Index
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Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Meerschaert, Mark M. Stochastic Models for Fractional Calculus Berlin/Boston : De Gruyter, Inc.,c2011 9783110258691
主題 Fractional calculus.;Diffusion processes.;Stochastic analysis
Electronic books
Alt Author Sikorskii, Alla
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