# On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos

## TL;DR

This paper investigates the conditions under which certain two-dimensional vectors in the second Wiener chaos are infinitely divisible, providing necessary and sufficient criteria and exploring specific cases involving Gaussian squares.

## Contribution

It offers new necessary and sufficient conditions for infinite divisibility of vectors in the second Wiener chaos, including detailed analysis of Gaussian square sums.

## Key findings

- Necessary and sufficient conditions for infinite divisibility.
- Easier verifiable sufficient conditions provided.
- Conjecture that vectors with Gaussian square sums are infinitely divisible.

## Abstract

Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility is presented as well as more easily verifiable sufficient conditions. The case where both components consist of a sum of two Gaussian squares is treated in more depth, and it is conjectured that such vectors are infinitely divisible.