Consider a reversible Markov chain with transition probabilities Pij? and limiting probabilities ?i?. Also consider the same chain truncated to the states 0,1,,M. That is, the transition probabilities {Pij??} of the truncated chain are Pij??=?????k=0m?Pik?Pij??,0,?0?i,j?M,elsewhere.? Show that the truncated chain is also reversible and has solutionspile.com

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Consider a reversible Markov chain with transition probabilities Pij? and limiting probabilities ?i?. Also consider the same chain truncated to the states 0,1,,M. That is, the transition probabilities {Pij??} of the truncated chain are Pij??=?????k=0m?Pik?Pij??,0,?0?i,j?M,elsewhere.? Show that the truncated chain is also reversible and has limiting probabilities given by ??i?=?k=0M??i??m=0M?Pkm??i??j=0M?Pij?? solutionspile.com

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