We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their appl...We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.展开更多
For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-m...For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-matrix of P（t）, is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegnmnd dual of some Q-function is also given.展开更多
文摘We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.
基金Supported by NSFC(Grant Nos.11626245 and 11571043)
文摘For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-matrix of P（t）, is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegnmnd dual of some Q-function is also given.
