Theoretical Statistics and Mathematics Unit, ISI Delhi

October 12, 2011 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Thomas Kaijser,
Linköping University, Sweden

Title:
On the conditional distributions of a partially observed Markov chain

Abstract of Talk

Let $X_n, n=0,1,2,...$ be an aperiodic positively recurrent Markov chain. Let $Y_n$ be an observation of $X_n$ at time $n$ obtained by an observation system which is not perfect. ($X_n$ is partially observed.)
Let $Z_n$ denote the conditional distribution of $X_n$ given all the observations up to time $n$. ($Z_n$ is thus a stochastic variable with values in the set of probability vectors on the state space of the Markov chain.)
Let $\mu_n$ denote the distribution of $Z_n$. Does it follow that there always exists a unique probability measure $\mu$ such that $\mu_n$ converges in distribution towards $\mu$ ? (Generalised version of Blackwell's conjecture from 1957.)