# Lamperti type theorems for random fields

## TL;DR

This paper extends Lamperti type theorems to ${f R}^m$-valued random fields, exploring their self-similarity, domains of attraction, and transformations linking self-similarity with stationarity, along with multivariate regular variation.

## Contribution

It introduces new results on self-similar random fields in ${f R}^m$, their domains of attraction, and Lamperti transformations, expanding existing theoretical frameworks.

## Key findings

- New results on self-similar ${f R}^m$-valued fields
- Characterization of domains of attraction for these fields
- Analysis of multivariate regularly and slowly varying functions

## 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 $\{{\bf X} ({\bf t}), \ {\bf t} \in {\mathbb R}^d \}$, 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.