Stochastics and Finance Seminar: Bohdan Maslowski -- Stochastic PDEs

SPEAKER: Bohdan Maslowski, Charles University, Prague, 

TITLE: Linear stochastic PDEs driven by Volterra processes 

TIME: December 10, 2-3.30 

VENUE: Grid room (830) 

ABSTRACT.  In the first part, the basic setting for infinite-dimensional linear
stochastic equations with memory-dependent noise will be recalled and some results on
existence, uniqueness, regularity and large time behaviour of solutions will be
presented.  The general results will be illustrated by examples of the most most popular
Volterra processes, such as fractional Brownian motion and Rosenblatt process.  

In the second part, some optimal control problems for such systems will be discussed for
the case of quadratic cost functionals.  We will also cosnider the Kalman-Bucy type
filter and the corresponding integral equations will be derived for the optimal estimate
and covariance of the error.  All results will be compared to the standard case of
Gauss-Markov driving processes.  

The talk is based on joint papers with P.  Coupek and V.  Kubelka.