Renewal theory with fat-tailed distributed sojourn times: Typical versus rare

@article{Wang2018RenewalTW,
  title={Renewal theory with fat-tailed distributed sojourn times: Typical versus rare},
  author={Wanli Wang and Johannes H. P. Schulz and Weihua Deng and Eli Barkai},
  journal={Physical Review E},
  year={2018}
}
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate function approach from large deviation theory does not hold and new tools must be considered. Here we investigate the large deviations of the number of renewals, the forward and backward recurrence time, the occupation time, and the time interval straddling… 
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