Strong limit theorems for anisotropic self-similar fields (Q486868)

In the present paper, the authors present three different definitions of self-similar fields and establish the interconnections between them. The definitions of fractional Brownian fields and sheets are also given in the paper. They consider fields which are self-similar with respect to every coordinate with individual Hurst index (such fields are usually called anisotropic, and in the Brownian case, Brownian sheets). The main results of the paper consist in the investigations of the asymptotic growth (strong limit theorems) of the sample paths of these fields.