| Description |
1 online resource (304 pages). |
|
text file |
| Series |
De Gruyter studies in mathematics,
0179-0986 ;
43
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De Gruyter studies in mathematics ; 43.
0179-0986
|
| Contents |
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. |
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4.3 Continuous time random walks4.4 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. |
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7.3 Tempered fractional derivatives7.4 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. |
| Summary |
This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. We will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. The book covers basic limit theorems for random variables and random vectors with heavy tails. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. |
| Bibliography |
Includes bibliographical references and index. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Fractional calculus.
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Fractional calculus. |
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Diffusion processes.
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Diffusion processes. |
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Stochastic analysis.
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Stochastic analysis. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Added Author |
Sikorskii, Alla.
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| Other Form: |
Print version: Meerschaert, Mark M. Stochastic Models for Fractional Calculus. Berlin : De Gruyter, ©2011 9783110258691 |
| ISBN |
9783110258165 (electronic book) |
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3110258161 (electronic book) |
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3110258692 |
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9783110258691 |
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