Speaker: Prof. David Nualart
David Nualart received his PhD from the University of Barcelona in 1975. He was professor at the University of Barcelona until 2005 when he joined the University of Kansas. Since 2012 he is the Black-Babcock Distinguished Professor at the University of Kansas. He has served in the editorial board of several top journals in probability and applied mathematics and he was the editor-in-chief of Communications in Probability from 2006 to 2008.
His main field of research is stochastic analysis, where he has made many contributions in a wide range of topics including stochastic partial differential equations, fractional Brownian motion, Malliavin calculus and rough path analysis.
He is the author of a reference book on “The Malliavin Calculus and Related Topics”, published by Springer in 2005 (2nd edition).
The Malliavin calculus or stochastic calculus of variations is a differential calculus on a Gaussian space, that was introduced by Paul Malliavin in the 70’s to provide a probabilistic proof of Hörmander’s hyopellipticity theorem. In this lecture we will present a gentle introduction to this calculus starting with the finite dimensional case and moving later to functionals of the Brownian motion.
We will describe the application of Malliavin calculus to establish the existence and smoothness of probability densities and its connection with the classical Itô calculus.
The role of Malliavin calculus on the geometric characterization of independence will be also discussed.