Consider a time-reversible Markov chain with transition probabilities P,, and limiting probabilities #,, and now consider the same chain trun- cated to the states 0, 1, ., M. That is, for the truncated chain its transition probabilities P, are

(P + Pk 0i M,j=i " k>M P = P (0, 0ij M otherwise. Show that the truncated chain is also time reversible and has limiting probabilities given by = M T, 2=0