Chung's law of the iterated logarithm for anisotropic Gaussian random fields (Q613179)

Let \(X(t), t\) an \(n\)-dimensional variable, be a Gaussian random field with stationary increments, and \(X(0) = 0\). Under some assumptions on the growth of the expected value of quadratic increments of \(X(t)\), the authors establish an iterated logarithm theorem. This theorem is applied to a variety of problems associated with Gaussian random fields with stationary increments and to solving a fractional heat equation. the authors describe in detail the properties of Gaussian fields and give a representation formula which formula is fundamental tool in their proofs and applications.