Nonlinear Filtering and Large Deviations: A PDE-Control Theoretic Approach,
Abstract
We consider the asymptotic nonlinear filtering problem dx = f(x) dt + sq. rt. epsilon, dy = h(x) dt + sq. rt. epsilon, and obtain the limit as epsilon approaches 0 of epsilon log (q(xt) to the epsilon power) = - W(x, t) for unnormalised conditional densities (q(x,t)) to the epsilon power, using PDE methods. Here, W(x,t) is the value function for a deterministic optimal control problem arising in Mortensen's deterministic estimation, and is the unique viscosity solution of a Hamilton-Jacobi- Bellman equation. Hijab has also studied this filtering problem, and we extend his large deviation result for certain unnormalised conditional measures. The resulting variational problem corresponds to the above control problem.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 26, 1987
- Accession Number
- ADA187436
Entities
People
- J. S. Baras
- Michael R. James
Organizations
- University of Maryland