UID:
almahu_9947359867402882
Umfang:
Online-Ressource
,
Online Ressource (291 S.)
Ausgabe:
1. Aufl.
ISBN:
3110258692
Inhalt:
Alla Sikorskii
Inhalt:
This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. The reader 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
Anmerkung:
Description based upon print version of record
,
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;.
,
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.
Weitere Ausg.:
ISBN 3110258161
Weitere Ausg.:
ISBN 9783110258165
Sprache:
Englisch
Schlagwort(e):
Electronic books
DOI:
10.1515/9783110258165
URL:
http://www.degruyter.com/doi/book/10.1515/9783110258165
