1.*11. Suppose that for a homogeneous Markov process the initial distri bution has support in NO as a subset of ::JJ?1, and that for each i E NO, the transition probability function P(i, .), also has support in NO. Thus is an infinite matrix called the "transition matrix". Show that p(n) as a matrix is just the nth power of p(1). Express the probability 9'{Xtk = ik, 1 .:s k .:s n}
in terms of the elements of these matrices. [This is the case of homogeneous Markov chains.]