0
votes
1answer
19 views

A problem on Markov process

Suppose, $\Pi_{\theta}$ be the transition probability function of a Markov chain. For any function $f$ define $$\Pi_{\theta}f_{\theta}(x) = \int f(y,\theta)\Pi_{\theta}(x,dy).$$ Is there any ...
3
votes
0answers
133 views

Generalization of Dobrushin's Ergodic Decomposition for continuous Markov Chains

Let $T$ be the shift transformation. Let $P$ be invariant for $T$ and also define a discrete state space Markov Chain. Let $C_{1},\ldots,C_{n}$ be the connected components of the Markov Chain. It ...
0
votes
0answers
237 views

How to calculate the limit kernel of a non-ergodic Markov Chain?

This question is about finding the limit kernel $P^\infty$ of a non-ergodic Markov Chain. The problem We consider a TDMC (Time Discrete Markov Chain) $(X_t)_{t \geq 0}$ with $X \in \mathcal{X}$ ...
0
votes
1answer
117 views

Manipulating ergodic Markov chains in order to make them non-ergodic

Consider a Markov chain, for simplicity let us consider time discrete chains. The problem We consider a TDMC (Time Discrete Markov Chain) $(X_t)_{t \geq 0}$ with $X \in \mathcal{X}$ (having ...