# PROBABILITY SEMINAR

## Monday, 19 November, 2012

**SPEAKER: **Prof. Jan Rosinski

TITLE:Wiener chaos, Malliavin calculus, and the Central Limit Theorem, Part 2.

**ABSTRACT**: Wiener-Ito chaos expansion has some analogy with Taylor's expansion in the classical analysis. Building on this analogy we will describe the Malliavin derivative (the gradient operator) and the divergence operator (Skorohod integral), which are the fundamental notions of the Malliavin calculus. Using these tools, a simple proof characterizing the asymptotic independence of Wiener chaos can be obtained. This, in turn, yields a simple proof of a multidimensional version of the celebrated Central Limit Theorem for Wiener chaos, the so called fourth moment theorem of Nualart and Peccati.