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Small deviations for the Poisson process

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  • Alvarez-Andrade, Sergio

Abstract

Let be a Poisson process, we study the asymptotic estimates for probabilities of the form , where r> 0, [latin small letter f with hook] [set membership, variant] K where K is the Strassen's set and at is a real sequence satisfying suitable conditions of growth and regularity. This type of result for Poisson process seems new. Finally, we establish a result of Chung's type for the Poisson process.

Suggested Citation

  • Alvarez-Andrade, Sergio, 1998. "Small deviations for the Poisson process," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 279-285, March.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:3:p:279-285
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    References listed on IDEAS

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    1. Horváth, Lajos, 1984. "Strong approximation of renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 18(1), pages 127-138, September.
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