Thomas Kaijser: On partially observed Markov chains

Let {X(n)} denote a Markov chain and {Y (n)} denote a sequence of “partial” observations of the {X(n)} process. Let Z(n) denote the conditional distribution of X(n) given the partial observation {Y (m), m = 1, 2, . . . , n}. The process {Z(n)} is often called the filtering process.

The purpose of this talk is to present a limit theorem for the distribution of Z(n) for the case when the state space of X(n) is denumerable.