Lamperti type theorems for random fields

Abstract

In the paper we consider Lamperti type theorems for random fields. Together with known results we present some new results on ${\mathbb{R}}^m$-valued self-similar fields $\{\mathbf{X}(\mathbf{t}),\mathbf{t}\in {\mathbb{R}}^d\}$, their domains of attraction and the so-called Lamperti transformations, expressing the relation between self-similarity and stationarity. Also we investigate regularly and slowly varying functions of several variables.