ore
16:00
presso Aula Cremona
In 1976 Paul Malliavin proposed in the paper "Stochastic calculus of
variation and hypoelliptic operators"
a probabilistic proof of Hormander's "sum of square" theorem. His proof
was based on a new infinite dimensional
differential calculus on the Wiener space. The theory was further
developed by Stroock, Bismut and Watanabe, among others,
to become what is nowadays known as the Malliavin calculus. This calculus
has become a fundamental tool in the theory of
stochastic (partial) differential equations and has found important
applications in mathematical finance.
This short course aims to provide a coincise introduction to the subject
together with a sketch of Malliavin's
proof of Hormander's theorem. Few remarks on the applications in
mathematical finance will also be provided.