There are three main areas of proposed activity. The first one is developing the technique based on quasiderivatives of solutions of Ito's equations and applying it for processes considered up to the first exit time from domains. The second area is investigating smoothness of solutions of SPDEs arising in filtering problems and the theory of measure--valued processes in order to be able to guarantee certain rates of convergence of approximations to their solutions. The third area is estimating the rate of convergence of numerical approximations for degenerate controlled diffusion processes.
The project relates to investigations of probabilistic behavior of certain objects. Part 1 is aimed at a better understanding of averaged quantities related to optimal control of random processes. Part 2 aims at problems directly related to many practical issues such as image reconstruction or high-performance computing in eliminating "friendly fire." It is also vital in dealing with problems like evolution of bacteria population which may be important in biotechnology. Part 3 deals with practical ways of solving problems of optimal control of random processes which arise for instance in finance.
