Question: 4.4.3 Consider a random walk Markov chain on state 0;1; : : : ;N with transition probability matrix where pi Cqi D 1;pi > 0;qi

4.4.3 Consider a random walk Markov chain on state 0;1; : : : ;N with transition probability matrix

0 1 23 00000 0 1 2 3 4 5 10 0

where pi Cqi D 1;pi > 0;qi > 0 for all i.
The transition probabilities from state 0 and N “reflect” the process back into state 1;2; : : : ;N ????1. Determine the limiting distribution.

0 1 23 00000 0 1 2 3 4 5 10 0 91 0 P1 0 92 0 P2 0 93 0 P3 40002 500O N-1 N 0 0 0 0 0 0 0 0 0 N-1 0 0 0 N 0 000 0 0 0 0 0 ... 0 PN-1 10

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