Journal of Applied Probability

Sample path large deviations of Poisson shot noise with heavy-tailed semiexponential distributions

Ken R. Duffy and Giovanni Luca Torrisi

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Abstract

It is shown that the sample paths of Poisson shot noise with heavy-tailed semiexponential distributions satisfy a large deviation principle with a rate function that is insensitive to the shot shape. This demonstrates that, on the scale of large deviations, paths to rare events do not depend on the shot shape.

Article information

Source
J. Appl. Probab., Volume 48, Number 3 (2011), 688-698.

Dates
First available in Project Euclid: 23 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1316796907

Digital Object Identifier
doi:10.1239/jap/1316796907

Mathematical Reviews number (MathSciNet)
MR2884808

Zentralblatt MATH identifier
1230.60025

Subjects
Primary: 60F10: Large deviations

Keywords
Heavy-tailed distribution sample path large deviation Poisson shot noise

Citation

Duffy, Ken R.; Torrisi, Giovanni Luca. Sample path large deviations of Poisson shot noise with heavy-tailed semiexponential distributions. J. Appl. Probab. 48 (2011), no. 3, 688--698. doi:10.1239/jap/1316796907. https://projecteuclid.org/euclid.jap/1316796907


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References

  • Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular Variation. Cambridge University Press.
  • Borovkov, A. A. (2002). On subexponential distributions and the asymptotics of the distribution of the maximum of sequential sums. Sibirsk. Mat. Zh. 43, 1235–1264.
  • Dembo, A. and Zeitouni, O. (1998). Large Deviations Techniques and Applications (Appl. Math. 38), 2nd edn. Springer, New York.
  • Ganesh, A., Macci, C. and Torrisi, G. L. (2005). Sample path large deviations principles for Poisson shot noise processes, and applications. Electron. J. Prob. 10, 1026–1043.
  • Ganesh, A. and Torrisi, G. L. (2006). A class of risk processes with delayed claims: ruin probability estimates under heavy tail conditions. J. Appl. Prob. 43, 916–926.
  • Gantert, N. (1998). Functional Erdős-Renyi laws for semiexponential random variables. Ann. Prob. 26, 1356–1369.
  • Klüppelberg, C. and Mikosch, T. (1995). Delay in claim settlement and ruin probability approximations. Scand. Actuarial J. 1995, 154–168.
  • Konstantopoulos, T. and Lin, S.-J. (1998). Macroscopic models for long-range dependent network traffic. Queueing Systems 28, 215–243.
  • Lowen, S. B. and Teich, M. C. (1990). Power-law shot noise. IEEE Trans. Inf. Theory 36, 1302–1318.
  • Rice, S. O. (1944). Mathematical analysis of random noise. Bell System Tech. J. 23, 282–332.
  • Stabile, G. and Torrisi, G. L. (2010). Large deviations of Poisson shot noise processes under heavy tail semi-exponential conditions. Statist. Prob. Lett. 2010, 1200–1209.