| Description |
1 online resource (x, 294 pages) : illustrations |
| Series |
De Gruyter studies in mathematics, 0179-0986 ; 43 |
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De Gruyter studies in mathematics ; 43. 0179-0986
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| Contents |
Introduction ; The traditional diffusion model -- Fractional diffusion -- Fractional derivatives ; The Grünwald formula -- More fractional derivatives -- The Caputo derivative -- Time-fractional diffusion -- Stable limit distributions ; Infinitely divisible laws -- Stable characteristic functions -- Semigroups -- Poisson approximation -- Shifted Poisson approximation -- Triangular arrays -- One-sided stable limits -- Two-sided stable limits -- Continuous time random walks ; Regular variation -- Stable central limit theorem -- Continuous time random walks -- Convergence in Skorokhod space -- CTRW governing equations -- Computations in R ; R codes for fractional diffusion -- Sample path simulations |
|
Vector fractional diffusion ; Vector random walks -- Vector random walks with heavy tails -- Triangular arrays of random vectors -- Stable random vectors -- Vector fractional diffusion equation -- Operator stable laws -- Operator regular variation -- Generalized domains of attraction -- Applications and extensions ; LePage series representation -- Tempered stable laws -- Tempered fractional derivatives -- Pearson diffusions -- Fractional Pearson diffusions -- Fractional Brownian motion -- Fractional random fields -- Applications of fractional diffusion -- Applications of vector fractional diffusion |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 279-288), and index |
| Notes |
In English |
|
Print version record |
| Subject |
Fractional calculus.
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Diffusion processes.
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Stochastic analysis.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Diffusion processes
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Fractional calculus
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Stochastic analysis
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Stochastische Analysis
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Anomale Diffusion
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Gebrochene Analysis
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Gebrochene Analysis.
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Stochastische Analysis.
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Stochastisches Modell.
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Diffusion.
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| Form |
Electronic book
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| Author |
Sikorskii, Alla., author
|
| LC no. |
2011036413 |
| ISBN |
9783110258165 |
|
3110258161 |
|
3110258692 |
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9783110258691 |
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9783110559149 |
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3110559145 |
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