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Long strange segments, ruin probabilities and the effect of memory on moving average processes

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  • Ghosh, Souvik
  • Samorodnitsky, Gennady

Abstract

We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. The rates are computed explicitly. We show that the rates are very similar to those of an i.i.d. process as long as the moving average coefficients decay fast enough. If they do not, then the rates are significantly different. This demonstrates the change in the length of memory in a moving average process associated with certain changes in the rate of decay of the coefficients.

Suggested Citation

  • Ghosh, Souvik & Samorodnitsky, Gennady, 2010. "Long strange segments, ruin probabilities and the effect of memory on moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2302-2330, December.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:12:p:2302-2330
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    References listed on IDEAS

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    3. T. Rachev, Svetlozar & Samorodnitsky, Gennady, 2001. "Long strange segments in a long-range-dependent moving average," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 119-148, May.
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    5. Hüsler, J. & Piterbarg, V., 2004. "On the ruin probability for physical fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 113(2), pages 315-332, October.
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