Markov积分算子半群的限制及关于增加积分算子半群的生成(英文)

Restriction of Markov Integrated Semigroups and Generation of Increasing Integrated semigroups

证明了转移函数是l∞的一个子空C1上的正的压缩C0半群,其极小生成元恰好是Markov积分算子半群的生成元在C1中的部分;Markov积分算子半群的生成元稠定的充分必要条件是q-矩阵Q一致有界;同时转移函数是Feller-Reuter-Riley的充要条件是Markov积分算子半群的生成元在c0中的部分产生一个强连续半群.最后,在序Banach空间给出了增加的压缩积分算子半群的生成定理.

We prove that the transition function is a positive contraction C. semigroup on a subspace C^1 of l∞. We obtain that the generator of the Markov integrated semigroup is densely defined in l∞ if and only if q- matrix Q is uniformly bounded. At the same time, a sufficient and necessary condition for a transition function to a Feller-Reuter-Riley transition function, is also given. Finally, in an ordered Banach space, a generation theorem is obtained for the increasing integrated semigroup of contractions.