演講訊息 TALKS

In this talk, we give a product formula of Hermite polynomials and show the relation between the real Wiener-Itô chaos and the complex Wiener-Itô chaos (or: multiple integrals), and then we extent the fourth moment theorem (or say: Nualart-Peccati criterion) to the complex multiple Wiener-Itô integrals. We also prove that the complex Hermite polynomials (or say: Hermite-Laguerre-Itô polynomials) are the eigenfunctions of complex Ornstein-Uhlenbeck operators. This talk is based on the following joint articles with Yong CHEN (陳勇). [1] Chen, Y., Liu Y., On the eigenfunctions of the complex Ornstein-Uhlenbeck operators, Kyoto J. Math., Vol. 54(3), 577-596, (2014) [2] Chen Y., Liu Y., On the fourth Moment Theorem for the Complex Multiple Wiener-Itô Integrals, Preprint (2015)