Small ball probabilities for Gaussian processes with stationary increments under Hölder norms

DOI10.1007/BF02212884zbMath0820.60023OpenAlexW2018836913MaRDI QIDQ1890742

Wenbo V. Li, James Kuelbs, Qui-Man Shao

Publication date: 23 May 1995

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02212884

zbMATH Keywords

fractional Brownian motionlaw of iterated logarithmstationary incrementssmall ball Gaussian probabilities

Mathematics Subject Classification ID

Gaussian processes (60G15)

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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
• Some exact equivalents for Brownian motion in Hölder norm
• The Gaussian measure of shifted balls
• 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
• Lim inf results for Gaussian samples and Chung's functional LIL
• A relation between Chung's and Strassen's laws of the iterated logarithm
• On Multivariate Normal Probabilities of Rectangles: Their Dependence on Correlations