35. Consider a time reversible continuous-time Markov chain having infinitesimal transition rates qij and limiting probabilities {Pi}. Let A denote a set of states for this chain, and consider a new continuous-time Markov chain with transition rates q∗

ij given by q∗

ij =



cqij , if i ∈ A, j /∈ A qij , otherwise where c is an arbitrary positive number. Show that this chain remains time reversible, and find its limiting probabilities.