*Mini course announcement*

Prof. Adrian Zalinescu [ Universitatea Alexandru Ioan Cuza - Iaşi, Romania ] will give a mini course on *Introduction to Stochastic Partial Di fferential Equations* (with applications to Finance, Biology, etc.), according with the following calendar 13 - 20 - 27 of March (2017) time table: from 1430 to 1730

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

__ Luca Di Persio - PhD assistant professor of Probability and Mathematical Finance

Dept. Informatics University of Verona strada le Grazie 15 - 37134 Verona - Italy Tel : +39 045 802 7968

Dept. Math University of Trento V. Sommarive, 14 - 38123 Povo - Italy Tel : +39 0461 281686