Nikolai Dokuchaev, (Trent University)


Title:  SPDEs and non-Markov Ito processes in bounded domains



Problems arising for non-Markov processes and their first exit times will be discussed. It is suggested a way of obtaining representation theorems for non-Markov processes via backward SPDEs (stochastic partial differential equations). For this purpose, some new regularity is obtained for solutions of SPDEs. More precisely, an analog of the second energy inequality and the related existence theorem are obtained for equations in domains with boundary.