In this paper,using the theorem of matrix semigroup and integrated semigroup,we mainly study the questions of continuous time Markov chains.First of all,we define a new semigroup on l_∞——w~*continuous matrix semigroup and obtain the Hille-Yosida theorem.Then,we apply the theorem of w~*continuous matrix semigroup to continuous time Markov chains.By studying the transition function,we obtain the one-to-one relationship between transition function and positive w~*continuous matrix contract semigroup,get the necessary and sufficient conditions of the transition function satisfy Kolmogorov forward and backward equations,and show for a stable Q matrix,under what condition the minimal q-function is Feller.What's more,in this paper,we diction the properties of Markov integrated semigroup. i.e.the property of honest and twice differentiable.
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