By Ramjan Ali

Abstract 

The switching diffusion is a continuous-time dynamics, having continuous paths and is driven by Brownian motion along with a continuous-time random process on a discrete set of regimes. Due to the coupled nature of randomness, the estimation of the unobserved regime based on the observed continuous dynamics remains a challenging problem. In this talk, I will first discuss the mathematical method for state estimation, where the law of the process is assumed to be known. A novel and shorter derivation, based on the semigroup theory is explored in this part. After that, I will present two data-driven approaches for estimation, by assuming the absence of knowledge of the law but the presence of labelled data. The first approach will be fully structure-free without any theoretical results, and the second approach will integrate the theoretical insight into its design, for which an approximation bound and convergence results are established. The performance of all three will be illustrated using some numerical examples.