..., 9. Theorem 18 (page 261) says that any regular stochastic matrix A has a unique steady-state vector w. Further, if

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9 Theorem 18 Page 261 Says That Any Regular Stochastic Matrix A Has A Unique Steady State Vector W Further If 1 (218.55 KiB) Viewed 19 times

..., 9. Theorem 18 (page 261) says that any regular stochastic matrix A has a unique steady-state vector w. Further, if xo is any initial state and Xk+1 = Axk for k= 0, 1, 2, then the Markov chain {xk} converges to w as k→ 00. This example seems to have sequences that converge to different steady- state vectors depending on the initial state. Explain the apparent contradiction. 10. Shade the region on the graph that corresponds to all the probability vectors. Use the graph to show that every Markov chain will converge to the same steady-state vector w and find w. 11. Find an algebraic description of the set of probability vectors in terms of vi and v2. Use this to show that every Markov chain will converge to the steady-state vector w.