Limit theorems for continuous-time random walks with infinite mean waiting times

@article{Meerschaert2004LimitTF,
  title={Limit theorems for continuous-time random walks with infinite mean waiting times},
  author={Mark M. Meerschaert and Hans-Peter Scheffler},
  journal={Journal of Applied Probability},
  year={2004},
  volume={41},
  pages={623 - 638}
}
A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Lévy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We… 

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