Small deviations for the Poisson process

DOI10.1016/S0167-7152(97)00128-4zbMath1246.60033OpenAlexW4238152276MaRDI QIDQ5891757

Sergio Alvarez-Andrade

Publication date: 2 September 2012

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(97)00128-4

zbMATH Keywords

Poisson processlaw of iterated logarithmChung's theoremsmall balls estimates

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Cites Work

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• Small ball estimates for Brownian motion and the Brownian sheet
• A note on small ball probability of a Gaussian process with stationary increments
• A lim inf result in Strassen's law of the iterated logarithm
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• Strong approximation of extended renewal processes
• Small values of Gaussian processes and functional laws of the iterated logarithm
• Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm
• Clustering behavior of finite variance partial sum processes
• Lim inf results for Gaussian samples and Chung's functional LIL
• A relation between Chung's and Strassen's laws of the iterated logarithm
• An invariance principle for the law of the iterated logarithm
• Maxima of partial sums of independent random variables
• On the Maximum Partial Sums of Sequences of Independent Random Variables

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