This talk will be delivered in person.
Uniqueness of the solution of generalized filtering equations in spaces of measures
We consider a generalized form of the filtering problem, where the diffusion matrix of the observation process may vanish, and all coefficients depend upon the current observation. We establish the filtering equations (both for the normalized and the “unnormalized” conditional law of the signal, given past observations), and prove that both have a unique measure-valued solution. The proof exploits a type of duality argument, where the dual process is the solution of a system of backward stochastic partial differential equations.
This is joint work with Dan Crisan.
The talk will be followed by refreshments in the Huxley Common Room at 4pm.