Small deviations for the Poisson process

Sergio Alvarez-Andrade

Statistics & Probability Letters, 1998, vol. 37, issue 2, 195-201

Abstract: Let be a Poisson process, we study the asymptotic estimates for probabilities of the form P(||Ñt--atf||[infinity][less-than-or-equals, slant]at-1r), where r> 0, f [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.

Keywords: Poisson; process; Small; balls; estimates; Chung's; Theorem; Law; of; iterated; logarithm (search for similar items in EconPapers)
Date: 1998
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