Speaker
Bohdan Maslowski, Charles University
AbstractIn the first part of the talk, some basic results of integration theory with respect to finite and infinite dimensional Volterra processes are recalled. The main examples are fractional Brownian motions, Rosenblatt processes and, more generally, the Hermite processes. These results are applied to linear stochastic equations in infinite dimensions. Some existence and regularity results for solutions are given in a general setting and specified in the case of stochastic heat equations. In the second part, equivalence of laws induced by such linear SPDEs and related inference problems are discussed. Based on [2], a method for estimation of a drift parameter is proposed in the case when the equation is driven by Rosenblat process. It is shown that this approach does not work for the Gaussian drift. This problem is discussed in more detail. Most of this talk is based on results obtained jointly with Petr Coupek, Martin Ondrejat, Pavel Kriz, T. E. Duncan and B. Pasik-Duncan.