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The Resource Stochastic models for fractional calculus, Mark M. Meerschaert, Alla Sikorskii

Stochastic models for fractional calculus, Mark M. Meerschaert, Alla Sikorskii

Label
Stochastic models for fractional calculus
Title
Stochastic models for fractional calculus
Statement of responsibility
Mark M. Meerschaert, Alla Sikorskii
Creator
Contributor
Author
Subject
Language
eng
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
Member of
Cataloging source
EBLCP
http://library.link/vocab/creatorDate
1955-
http://library.link/vocab/creatorName
Meerschaert, Mark M.
Dewey number
515.83
Illustrations
illustrations
Index
index present
Language note
In English
LC call number
QA314 .M484 2011
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Sikorskii, Alla.
Series statement
De Gruyter studies in mathematics,
Series volume
43
http://library.link/vocab/subjectName
  • Fractional calculus
  • Diffusion processes
  • Stochastic analysis
  • MATHEMATICS
  • MATHEMATICS
  • Diffusion processes
  • Fractional calculus
  • Stochastic analysis
  • Gebrochene Analysis
  • Stochastische Analysis
  • Stochastisches Modell
  • Diffusion
Label
Stochastic models for fractional calculus, Mark M. Meerschaert, Alla Sikorskii
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 279-288), and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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
  • Introduction
  • 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
  • The traditional diffusion model
  • Fractional diffusion
  • Fractional derivatives
  • The Grünwald formula
  • More fractional derivatives
  • The Caputo derivative
  • Time-fractional diffusion
  • 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
  • Vector fractional diffusion
  • Applications of 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
Control code
772845223
Dimensions
unknown
Extent
1 online resource (x, 294 pages)
Form of item
online
Isbn
9783110258691
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1515/9783110258165
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
835465
Specific material designation
remote
System control number
(OCoLC)772845223
Label
Stochastic models for fractional calculus, Mark M. Meerschaert, Alla Sikorskii
Publication
Bibliography note
Includes bibliographical references (pages 279-288), and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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
  • Introduction
  • 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
  • The traditional diffusion model
  • Fractional diffusion
  • Fractional derivatives
  • The Grünwald formula
  • More fractional derivatives
  • The Caputo derivative
  • Time-fractional diffusion
  • 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
  • Vector fractional diffusion
  • Applications of 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
Control code
772845223
Dimensions
unknown
Extent
1 online resource (x, 294 pages)
Form of item
online
Isbn
9783110258691
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1515/9783110258165
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
835465
Specific material designation
remote
System control number
(OCoLC)772845223

Library Locations

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      1 University Blvd, St. Louis, MO, 63121, US
      38.710138 -90.311107
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