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

Meerschaert, Mark; Wang, Wensheng; Xiao, Yimin

doi:10.1090/S0002-9947-2012-05678-9

Fernique-type inequalities and moduli of continuity for anisotropic Gaussian random fields
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by Mark M. Meerschaert, Wensheng Wang and Yimin Xiao PDF

Trans. Amer. Math. Soc. 365 (2013), 1081-1107 Request permission

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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