all the lessons will  take place at the Dept. of Computer Science - UniVr
Strada le Grazie, 15 - Verona
Ca' Vignal 2,   first floor ,  Room M

located here

https://goo.gl/maps/Yx2JU

The tentative programme is the following:

1. Gaussian measure theory
Random vectors and Bochner integral. Some elements of probability in innite-dimensional
spaces are considered, with emphasis on the integration of random vectors with values in
separable Banach-spaces and in operator spaces.
Gaussian measures. We introduce cylindrical Gaussian random variables and Hilbert-spacevalued Gaussian random variables and then dene cylindrical Wiener processes and Q-Wiener processes (i.e. with the covariance given by the trace-class operator Q) in a natural way. Stochastic integral and Ito's formula. The stochastic integral is constructed with respect
to a cylindrical Wiener process, then with respect to a Q-Wiener process, by extending the
integral of elementary processes. Some properties of the stochastic integral are given, including Ito's formula.

2. Stochastic Di erential Equations
Semigroup Theory. In this section we review the fundamentals of semigroup theory.
Stochastic Convolutions and Linear SPDEs. We derive existence and uniqueness of di erent
types of solutions for linear SDEs driven by generators of C0-semigroups. The method is based on the study of the stochastic convolution. Solutions by Variational Method. The purpose is to study solutions of nonlinear SPDEs, which are seen as evolution equations in a Gelfand triplet, under assumptions of compact embedding or monotone coe cients.

3. Applications
Along the abstract study of SDEs in innite-dimensional spaces, various examples of SPDEs
with applications in physics, biology and mathematical finance will be given.

A detailed bibliograpy will be given during the course.

___________

Do not hesitate to contact me for further details: luca.dipersio@univr.it

LuCa