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From anomalous deterministic diffusion to the continuous time random walk / vorgelegt von Markus Niemann. 2009
Content
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
The uncoupled case
The coupled case
Derivation of equation (3.43)
Applications to other CTRW models
The Creeper model
Spectral properties of a model for weak ergodicity breaking
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
Convergence to an uncoupled CTRW
Convergence to a coupled 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
A symmetrized Manneville-Pomeau map
An asymmetric Manneville-Pomeau map
Summary and Outlook
List of specific results
Outlook
Renewal Equation Approach to Joint Probability Distributions
Power Series Expansion of a Determinant
Some Estimates for the Exponential Function
Bibliography
Acknowledgments