Lamperti-type theorems for random fields

Lamperti-type theorems for random fields are presented. Together with known results, some new results are put forward on $\mathbf{R}^m$-valued self-similar fields $\{\mathbf{X}(\mathbf{t}),\, \mathbf{t} \in \mathbf{R}^d \}$, their domains of attraction, and the so-called Lamperti transformations, expressing the relation between self-similarity and stationarity. Regularly and slowly varying functions of several variables are also investigated.