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Tail behavior of random products and stochastic exponentials

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  • Cohen, Serge
  • Mikosch, Thomas

Abstract

In this paper we study the distributional tail behavior of the solution to a linear stochastic differential equation driven by infinite variance [alpha]-stable Lévy motion. We show that the solution is regularly varying with index [alpha]. An important step in the proof is the study of a Poisson number of products of independent random variables with regularly varying tail. The study of these products merits its own interest because it involves interesting saddle-point approximation techniques.

Suggested Citation

  • Cohen, Serge & Mikosch, Thomas, 2008. "Tail behavior of random products and stochastic exponentials," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 333-345, March.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:3:p:333-345
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    References listed on IDEAS

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    1. Hult, Henrik & Lindskog, Filip, 2005. "Extremal behavior of regularly varying stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 249-274, February.
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