Optimal Filtering, Interpolation and Extrapolation of Markov Processes with a Countable Number of States

Abstract

The present chapter will be concerned with a pair of random processes (θ, ξ) = (θ _t , ξ _t ), 0 ≤ t ≤ T, where the unobservable component θ is a Markov process with a finite or countable number of states, and the observable process ξ permits the stochastic differential

$$d{\xi _t}\,{A_t}({\theta _t},\xi )dt\, + \,{B_t}(\xi )d{W_t},$$

(9.1)

where W _t is a Wiener process.