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All issues Volume 17 (2013) ESAIM: PS, 17 (2013) 567-591 References
Free Access
Issue
ESAIM: PS
Volume 17, 2013
Page(s) 567 - 591
DOI https://doi.org/10.1051/ps/2012010
Published online 01 August 2013
  1. J. Bertoin, Lévy Processes. Cambridge University Press, Cambridge (1996). [Google Scholar]
  2. H. Biermé, A. Estrade and I. Kaj, Self-similar random fields and rescaled random balls models. J. Theor. Prob. 23 (2010) 1110–1141. [Google Scholar]
  3. N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation. Cambridge University Press, Cambridge (1987). [Google Scholar]
  4. D.J. Daley and D. Vere-Jones, An introduction to the theory of point processes, in Elementary theory and methods I. Probab. Appl. 2nd edition. Springer-Verlag (2003). [Google Scholar]
  5. C. Dombry and I. Kaj, The on-off network traffic model under intermediate scaling. Queuing Syst. 69 (2011) 29–44. [CrossRef] [Google Scholar]
  6. R. Gaigalas. A Poisson bridge between fractional Brownian motion and stable Lévy motion. Stoch. Proc. Appl. 116 (2006) 447–462. [CrossRef] [Google Scholar]
  7. R. Gaigalas and I. Kaj, Convergence of scaled renewal processes and a packet arrival model. Bernoulli 9 (2003) 671–703. [CrossRef] [MathSciNet] [Google Scholar]
  8. G. Grimmett, Weak convergence using higher-order cumulants. J. Theor. Prob. 5 (1992) 767–773. [CrossRef] [Google Scholar]
  9. I. Kaj and A. Martin-Löf, Scaling limit results for the sum of many inverse Lévy subordinators. arXiv:1203.6831 [math.PR] (2012). [Google Scholar]
  10. I. Kaj and M.S. Taqqu, Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach, in: In an Out of Equilibrium 2, Progress Probability, vol. 60 edited by M.E. Vares and V. Sidoravicius. Birkhauser (2008) 383–427. [Google Scholar]
  11. O. Kallenberg. Foundations of Modern Probability, 2nd edition. Springer-Verlag, New York (2002). [Google Scholar]
  12. J.B. Lévy and M.S. Taqqu, Renewal reward processes with heavy-tailed interrenewal times and heavy-tailed rewards. Bernoulli 6 (2000) 23–44. [CrossRef] [MathSciNet] [Google Scholar]
  13. T. Mikosch, S. Resnick, H. Rootzen and A. Stegeman,Is network traffic approximated by stable Lévy motion or fractional Brownian motion. Ann. Appl. Probab. 12 (2002) 23–68. [Google Scholar]
  14. V. Pipiras and M.S. Taqqu, The limit of a renewal-reward process with heavy-tailed rewards is not a linear fractional stable motion. Bernoulli 6 (2000) 607–614. [CrossRef] [MathSciNet] [Google Scholar]
  15. V. Pipiras, M.S. Taqqu and J.B. Lévy, Slow, fast and arbitrary growth conditions for renewal reward processes when the renewals and the rewards are heavy-tailed. Bernoulli 10 (2004) 121–163. [CrossRef] [MathSciNet] [Google Scholar]
  16. S.I. Resnick, Extreme values, regular variation, and point processes. Springer, New York (1987). [Google Scholar]
  17. S.I. Resnick, Heavy-tail phenomena, Probabilistic and statistical modeling. Springer Series in Operations Research and Financial Engineering. Springer, New York (2007). [Google Scholar]
  18. G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian Random Processes. Chapman and Hall (1994). [Google Scholar]
  19. M.S. Taqqu, W. Willinger and R. Sherman, Proof of a fundamental result in self-similar traffic modeling. Comput. Commun. Rev. 27 (1997) 5–23. [CrossRef] [Google Scholar]
  20. J.L. Teugels, Renewal theorems when the first and the second moment is infinite. Ann. Math. Statist. 39 (1968) 1210–1219. [CrossRef] [MathSciNet] [Google Scholar]

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