Backward SDE method for nonlinear filtering problems

Applied and Computational Mathematics Seminar
Monday, October 17, 2016 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 005
Prof. Yanzhao Cao – Auburn University Mathematics
Martin Short
A nonlinear filtering problem can be classified as a stochastic Bayesian optimization problem of identifying the state of a stochastic dynamical system based on noisy observations of the system. Well known numerical simulation methods include unscented Kalman filters and particle filters. In this talk, we consider a class of efficient numerical methods based on forward backward stochastic differential equations. The backward SDEs for nonlinear filtering problems are similar to the Fokker-Planck equations for SDEs. We will describe the process of deriving such backward SDEs as well as high order numerical algorithms to solve them, which in turn solve nonlinear filtering problems.