2 Self-similarity, Stochasticity and Fractionality

Long-range Interactions, Stochasticity 作者：Albert C.J. Luo，V. Afraimovich　　 ISBN：978-7-04-029188-9　出版时间：2010-06-18

内封

版权

目录

front matter

1 Fractional Zaslavsky and H´enon Discrete Maps

2 Self-similarity, Stochasticity and Fractionality

3 Long-range Interactions and Diluted Networks

4 Metastability and Transients in Brain Dynamics: Problems and Rigorous Results

5 Dynamics of Soliton Chains: From Simple to Complex and Chaotic Motions

6 What is Control of Turbulence in Crossed Fields?–Don’t Even Think of Eliminating All Vortexes!

7 Entropy and Transport in Billiards

Index
- Vladimir V. Uchaikin
- 2.1 Introduction
- 2.1.1 Ten years ago
- 2.1.2 Two kinds of motion
- 2.1.3 Dynamic self-similarity
- 2.1.4 Stochastic self-similarity.
- 2.1.5 Self-similarity and stationarity
- 2.2 From Brownian motion to L`evy motion
- 2.2.1 Brownian motion
- 2.2.2 Self-similar Brownian motion in nonstationary nonhomogeneous environment
- 2.2.3 Stable laws
- 2.2.4 Discrete time L`evy motion
- 2.2.5 Continuous time L`evy motion
- 2.2.6 Fractional equations for continuous time L`evy motion
- 2.3 Fractional Brownian motion
- 2.3.1 Differential Brownian motion process
- 2.3.2 Integral Brownian motion process
- 2.3.3 Fractional Brownian motion
- 2.3.4 Fractional Gaussian noises
- 2.3.5 Barnes and Allan model
- 2.3.6 Fractional L`evy motion
- 2.4 Fractional Poisson motion
- 2.4.1 Renewal processes
- 2.4.2 Self-similar renewal processes
- 2.4.3 Three forms of fractal dust generator
- 2.4.4 nth arrival time distribution
- 2.4.5 Fractional Poisson distribution
- 2.5 Fractional compound Poisson process
- 2.5.1 Compound Poisson process
- 2.5.2 L`evy-Poisson motion
- 2.5.3 Fractional compound Poisson motion
- 2.5.4 A link between solutions.
- 2.5.5 Fractional generalization of the L`evy motion
- Acknowledgments
- Appendix. Fractional operators
- References

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