Fernique-type inequalities and moduli of continuity for anisotropic Gaussian random fields.
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.
Department of Statistics and Probability, Michigan State University, A-413 Wells Hall, East Lansing, MI 48824, USA.
Mark M
MM
Meerschaert
Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China.
Wensheng
W
Wang
Department of Statistics and Probability, Michigan State University, A-413 Wells Hall, East Lansing, MI 48824, USA.
Yimin
Y
Xiao
Gaussian random field; anisotropy; fractional Brownian sheet; law of the iterated logarithm; modulus of continuity