On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos
Open Access
- 28 August 2020
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 7 (3), 267-289
- https://doi.org/10.15559/20-vmsta160
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos, Authors: Andreas Basse-O’Connor, Jan Pedersen, Victor Rohde , 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.Keywords
This publication has 11 references indexed in Scilit:
- Characterization of positively correlated squared Gaussian processesThe Annals of Probability, 2014
- Markov Processes, Gaussian Processes, and Local TimesPublished by Cambridge University Press (CUP) ,2006
- A characterization of the infinitely divisible squared Gaussian processesThe Annals of Probability, 2006
- On the infinite divisibility of squared Gaussian processesProbability Theory and Related Fields, 2003
- Gaussian Hilbert SpacesPublished by Cambridge University Press (CUP) ,1997
- Association and infinite divisibility for the Wishart distribution and its diagonal marginalsJournal of Multivariate Analysis, 1991
- Characterization of infinitely divisible multivariate gamma distributionsJournal of Multivariate Analysis, 1984
- Non-central limit theorems for non-linear functional of Gaussian fieldsProbability Theory and Related Fields, 1979
- On the structure of the Wishart distributionJournal of Multivariate Analysis, 1976
- The arithmetical character of the Wishart distributionMathematical Proceedings of the Cambridge Philosophical Society, 1948