$Stochastic models for fractional calculus /$

Stochastic models for fractional calculus /

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Bibliographic Details
Author / Creator:	Meerschaert, Mark M., 1955-
Imprint:	Berlin : De Gruyter, ©2012.
Description:	1 online resource (x, 294 pages) : illustrations
Language:	English
Series:	De Gruyter studies in mathematics, 0179-0986 ; 43 De Gruyter studies in mathematics ; 43.
Subject:	Fractional calculus. Diffusion processes. Stochastic analysis. Diffusion processes. Fractional calculus. Stochastic analysis. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11123038

Hidden Bibliographic Details
Other authors / contributors:	Sikorskii, Alla., author.
ISBN:	9783110258165 3110258161 3110258692 9783110258691
Digital file characteristics:	data file
Notes:	Includes bibliographical references (pages 279-288), and index. In English. Print version record.
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.
Other form:	Print version: Meerschaert, Mark M., 1955- Stochastic models for fractional calculus. Berlin : De Gruyter, ©2011 9783110258691
Standard no.:	10.1515/9783110258165

Table of 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.