Nonlinear Filtering for Markov Systems with Delayed Observations

Abstract

Nonlinear Filtering for Markov Systems with Delayed ObservationsThis paper deals with nonlinear filtering problems with delays, i. e., we consider a system (X, Y), which can be represented by means of a system (X, Ŷ), in the sense thatYt= Ŷa(t), wherea(t)is a delayed time transformation. We start withXbeing a Markov process, and then study Markovian systems, not necessarily diffusive, with correlated noises. The interest is focused on the existence of explicit representations of the corresponding filters as functionals depending on the observed trajectory. Various assumptions on the functiona(t)are considered.