Wang, Teng2012-10-092012-10-092012-07https://hdl.handle.net/11299/135834University of Minnesota Ph.D. dissertation. July 2012. Major: Mathematics. Advisor: N.V. Krylov. 1 computer file (PDF); iii, 60 pages.We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional distribution of the first component before it hits the boundary and give a formula for the conditional distribution of the first component at the first time it hits the boundary. We also derive a formula for the conditional distribution of the exit time if the observation is always available.en-USFiltering equations in domainsStochastic partial differential equationsMathematicsThesis or Dissertation