Diffusion Processes and Partial Differential Equations

9876586拟议活动有三个主要领域。 第一个是开发的技术的基础上quasidifferentiators的解决方案的伊藤方程和应用它的过程中考虑到第一次退出时间域。 第二个领域是调查平滑的解决方案的SPDEs所产生的过滤问题和理论的措施-值的过程，以便能够保证一定的速度收敛的近似其解决方案。 第三个领域是估计退化控制扩散过程的数值近似的收敛速度。该项目涉及某些对象的概率行为的调查。 第1部分旨在更好地理解与随机过程最优控制相关的平均量。 第二部分针对与许多实际问题直接相关的问题，如图像重建或高性能计算，以消除“友军炮火”。“这对于处理细菌种群进化等问题也至关重要，这在生物技术中可能很重要。第3部分涉及解决随机过程的最优控制问题的实际方法，例如在金融领域。

9876586There 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.