Mathematical Finance and Stochastics Seminar by Daniel Noelck: Exponential Stability of Stochastic Filter via Non-Degeneracy and Analytic Stability of the Signal
Speaker: Daniel Noelck, senior research associate, Illinois Tech
Title: Exponential Stability of Stochastic Filter via Non-Degeneracy and Analytic Stability of the Signal
Abstract: Filter stability is a classical problem in the study of hidden Markov models. In such models, an incorrectly initialized non-linear filter is said to be stable if the filter corrects itself as more measurements are collected over time. In this talk, we will introduce the mathematical framework for both the discrete and continuous time stochastic filter. We review classical results that guarantee exponential stability under the "mixing condition." We will further discuss the limitations of such a condition, and propose new assumptions to obtain exponential stability through a non-degenerate observation and stability of the signal.
Stochastic Analysis