Stochastic Models for Fractional Calculus 2nd Edition by Mark M Meerschaert, Alla Sikorskii – Ebook PDF Instant Download/Delivery: 3110559072 ,9783110559071
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Product details:
ISBN 10: 3110559072
ISBN 13: 9783110559071
Author: Mark M Meerschaert, Alla Sikorskii
Stochastic Models for Fractional Calculus 2nd Edition Table of contents:
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 walks
4.4 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 The fractional Poisson process
7.2 LePage series representation
7.3 Tempered stable laws
7.4 Tempered fractional derivatives
7.5 Distributed order fractional derivatives
7.6 Pearson diffusions
7.7 Fractional Pearson diffusions
7.8 Correlation structure of fractional processes
7.9 Fractional Brownian motion
7.10 Fractional random fields
7.11 Applications of fractional diffusion
7.12 Applications of vector fractional diffusion
Bibliography
Index
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Tags: Mark M Meerschaert, Alla Sikorskii, Stochastic Models, Fractional Calculus


