Ciclo di Seminari - Progetto ERC PASCAL (Probabilistic and Statistical Techniques for Cosmological Applications)

Mercoledì 6 aprile ore 12:30

Aula D'Antoni Dipartimento di Matematica Università di Roma Tor Vergata

Speaker: Peter Eichelsbacher, Ruhr-Universität Bochum

Title: Malliavin-Stein method for Variance-Gamma approximation on Wiener space.

Abstract:

In a joint work with Christoph Thäle, we combine Malliavin calculus with Stein's method to derive bounds for the Variance-Gamma approximation of functionals of isonormal Gaussian processes, in particular of random variables living inside a fixed Wiener chaos induced by such a process. The bounds are presented in terms of Malliavin operators and norms of contractions. We show that a sequence of distributions of random variables in the second Wiener chaos converges to a Variance-Gamma distribution if and only if their moments of order two to six converge to that of a Variance-Gamma distributed random variable (six moment theorem). Moreover, simplified versions for Laplace or symmetrized Gamma distributions are presented. Also multivariate extensions and a universality result for homogeneous sums are considered.

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Valentina Cammarota Department of Mathematics Universita` degli Studi di Roma Tor Vergata http://www.mat.uniroma2.it/english.php https://sites.google.com/site/valentinacammarota/