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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Fernique-type inequalities and moduli of continuity for anisotropic Gaussian random fields


Authors: Mark M. Meerschaert, Wensheng Wang and Yimin Xiao
Journal: Trans. Amer. Math. Soc. 365 (2013), 1081-1107
MSC (2010): Primary 60G15, 60G17, 60F10, 60F15
Published electronically: August 1, 2012
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Abstract: This paper is concerned with sample path properties of anisotropic Gaussian random fields. We establish Fernique-type inequalities and utilize them to study the global and local moduli of continuity for anisotropic Gaussian random fields. Applications to fractional Brownian sheets and to the solutions of stochastic partial differential equations are investigated.


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Additional Information

Mark M. Meerschaert
Affiliation: Department of Statistics and Probability, Michigan State University, A-413 Wells Hall, East Lansing, Michigan 48824
Email: mcubed@stt.msu.edu

Wensheng Wang
Affiliation: Department of Mathematics, Hangzhou Normal University, Hangzhou, 310036, People’s Republic of China
Email: wswang@stat.ecnu.edu.cn

Yimin Xiao
Affiliation: Department of Statistics and Probability, Michigan State University, A-413 Wells Hall, East Lansing, Michigan 48824
Email: xiao@stt.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05678-9
PII: S 0002-9947(2012)05678-9
Keywords: Gaussian random field, anisotropy, fractional Brownian sheet, modulus of continuity, law of the iterated logarithm.
Received by editor(s): January 22, 2011
Received by editor(s) in revised form: July 27, 2011
Published electronically: August 1, 2012
Additional Notes: The research of the first author was supported by NSF grants DMS-0417869, DMS-0803360 and EAR-0823965.
The research of the second author was supported by NSFC grant 11071076 and NSF grant DMS-0417869.
The research of the third author was supported by NSF grant DMS-0706728.
The second author is the corresponding author for this paper
Article copyright: © Copyright 2012 American Mathematical Society