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.
Bibliographical noteFunding Information:
The work of the first author was partially supported by NSF Grant DMS-0653121 .
- Filtering equations in domains
- Stochastic partial differential equations