Phase Transitions in Nonlinear Filtering

Understand

It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information.

• While the existing theory provides a rather complete picture of classical filtering models, many infinite-dimensional problems are outside its scope.
• Far from being a technical issue, the infinite-dimensional setting gives rise to surprising phenomena and new questions in filtering theory.
• The aim of this paper is to discuss some elementary examples, conjectures, and general theory that arise in this setting, and to highlight connections with problems in statistical mechanics and ergodic theory.