On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos
Volume 7, Issue 3 (2020), pp. 267–289
Pub. online: 28 August 2020
Type: Research Article
Open Access
Open Access
Received
19 May 2020
19 May 2020
Revised
3 August 2020
3 August 2020
Accepted
16 August 2020
16 August 2020
Published
28 August 2020
28 August 2020
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 are 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.
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