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Upper tail probabilities of integrated Brownian motions
Univ Idaho, Dept Math, Moscow, ID 83844 USA.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
2015 (English)In: Science China Mathematics, ISSN 1674-7283, Vol. 58, no 5, 1091-1100 p.Article in journal (Refereed) Published
Abstract [en]

We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the L (p) norm. For the uniform norm, Talagrands approach is used, while for the L (p) norm, Zolotares approach together with suitable metric entropy and the associated small ball probabilities are used. This proposed method leads to an interesting and concrete connection between small ball probabilities and upper tail probabilities (large ball probabilities) for general Gaussian random variables in Banach spaces. As applications, explicit bounds are given for the largest eigenvalue of the covariance operator, and appropriate limiting behaviors of the Laplace transforms of m-times integrated Brownian motions are presented as well.

Place, publisher, year, edition, pages
Springer Verlag (Germany) , 2015. Vol. 58, no 5, 1091-1100 p.
Keyword [en]
integrated Brownian motion; upper tail probability; small ball probability; metric entropy
National Category
URN: urn:nbn:se:liu:diva-118019DOI: 10.1007/s11425-015-4981-9ISI: 000352993800009OAI: diva2:813149

Funding Agencies|Simons Foundation [246211]

Available from: 2015-05-21 Created: 2015-05-20 Last updated: 2015-05-21

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Yang, Xiangfeng
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Mathematical Statistics The Institute of Technology
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