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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
©2012
國際標準書號 9783110258165 (electronic bk.)
9783110258691
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
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob
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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