Theorem Of Semigroup And Application To Markov Chains

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.