Stochastic Models for Fractional Calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
2011
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 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 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 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 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 |
| Beschreibung: | 1 Online-Ressource (304 pages) |
| ISBN: | 3110258161 9783110258165 |
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| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
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| 650 | 4 | |a Fractional calculus | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Meerschaert, Mark M. |
| author_facet | Meerschaert, Mark M. |
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| dewey-full | 515.83 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.83 |
| dewey-search | 515.83 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043075417 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:40Z |
| institution | BVB |
| isbn | 3110258161 9783110258165 |
| language | English |
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| spelling | Meerschaert, Mark M. Verfasser aut Stochastic Models for Fractional Calculus Berlin De Gruyter 2011 1 Online-Ressource (304 pages) txt rdacontent c rdamedia cr rdacarrier 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 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 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 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 Calculus Mathematics MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Diffusion processes fast Fractional calculus fast Stochastic analysis fast Mathematik Fractional calculus Diffusion processes Stochastic analysis Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Anomale Diffusion (DE-588)4532384-7 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Anomale Dispersion (DE-588)4327175-3 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 s Anomale Dispersion (DE-588)4327175-3 s Stochastische Analysis (DE-588)4132272-1 s 1\p DE-604 Anomale Diffusion (DE-588)4532384-7 s 2\p DE-604 Sikorskii, Alla Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=430094 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Meerschaert, Mark M. Stochastic Models for Fractional Calculus Calculus Mathematics MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Diffusion processes fast Fractional calculus fast Stochastic analysis fast Mathematik Fractional calculus Diffusion processes Stochastic analysis Gebrochene Analysis (DE-588)4722475-7 gnd Anomale Diffusion (DE-588)4532384-7 gnd Stochastische Analysis (DE-588)4132272-1 gnd Anomale Dispersion (DE-588)4327175-3 gnd |
| subject_GND | (DE-588)4722475-7 (DE-588)4532384-7 (DE-588)4132272-1 (DE-588)4327175-3 |
| title | Stochastic Models for Fractional Calculus |
| title_auth | Stochastic Models for Fractional Calculus |
| title_exact_search | Stochastic Models for Fractional Calculus |
| title_full | Stochastic Models for Fractional Calculus |
| title_fullStr | Stochastic Models for Fractional Calculus |
| title_full_unstemmed | Stochastic Models for Fractional Calculus |
| title_short | Stochastic Models for Fractional Calculus |
| title_sort | stochastic models for fractional calculus |
| topic | Calculus Mathematics MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Diffusion processes fast Fractional calculus fast Stochastic analysis fast Mathematik Fractional calculus Diffusion processes Stochastic analysis Gebrochene Analysis (DE-588)4722475-7 gnd Anomale Diffusion (DE-588)4532384-7 gnd Stochastische Analysis (DE-588)4132272-1 gnd Anomale Dispersion (DE-588)4327175-3 gnd |
| topic_facet | Calculus Mathematics MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Diffusion processes Fractional calculus Stochastic analysis Mathematik Gebrochene Analysis Anomale Diffusion Stochastische Analysis Anomale Dispersion |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=430094 |
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