Star-Like Collage. Consider the Markov chain X n in Example 107 with the variation that the set S0 may consist of more that one state. In addition to the assumption that the chain restricted to each...

Star-Like Collage. Consider the Markov chain X_n
in Example 107 with the variation that the set S0 may consist of more that one state. In addition to the assumption that the chain restricted to each S0∪Sk is ergodic with stationary distribution p_k
i , assume the chain restricted to S0 is ergodic with stationary distribution p₀
i . Show that X_n
is ergodic and its stationary distribution isExample 107