From anomalous deterministic diffusion to the continuous time random walk / vorgelegt von Markus Niemann. 2009
Inhalt
- Introduction
- Preliminaries
- Probability Distributions
- Stochastic Processes
- The Continuous-Time Random Walk
- The Manneville-Pomeau Map
- Multi point properties of continuous-time random walks
- Introduction
- Joint Probability Distributions
- Multi Point Correlations
- Applications to other CTRW models
- Asymptotic behavior of continuous-time random walks
- Introduction
- Scaling Limit with Finite Mean Waiting Time
- Joint probability distributions with jump densities
- Asymptotic behavior of an independent CTRW
- Summary of Limits
- Nonindependent continuous-time random walks
- Introduction
- Nonindependent CTRWs with finite memory
- Asymptotic behavior for irreducible Markov chains
- The reducible Markov Chain
- Anomalous Deterministic Diffusion
- Introduction
- The basic setup
- Asymptotics for the dynamics of Smod(t)
- Discussion on the dynamic S(t)
- Application to Manneville-Pomeau maps
- Summary and Outlook
- Renewal Equation Approach to Joint Probability Distributions
- Power Series Expansion of a Determinant
- Some Estimates for the Exponential Function
- Bibliography
- Acknowledgments