Stochastic evolution equations and space-time systems

The project is aimed at research in the field of stochastic partial differential equations (SPDEs),
in particular, at the qualitative behaviour of solutions and optimal control thereof. Also, some
related space-time systems (Brownian web) arising as a continuum limit of discrete random
systems will be studied. More specifically, the following topics will be emphasized: 1. Non -
Markovian SPDEs, in which the driving noise is a general Volterra process that does not
necessarily have independent increments. Existence, uniqueness, regularity and large time
behaviour will be treated and the general results will be applied to fractional noises or the
Rosenblatt process. 2. Qualitative properties and numerical schemes for nonlinear SPDEs, for
example, equations with jumps, reaction-diffusion equations and Navier-Stokes equations,
nonlinear wave equations on flat spaces and Riemannian manifolds. 3. Optimal control of non-
Markovian systems described in item 1) . 4. Brownian web and its relations to stochastic flows.