一般突变过程诱导的积分半群(英文)

An Integrated Semigroup Induced by the General Catastrophe Process

研究了一般突变q-矩阵Q在l∞上生成一个压缩积分半群的充要条件,并且Q可在l∞上生成一最小的积分Q-半群T(t),讨论了T(t)单调的充要条件,给出了T(t)是Feller的充分条件,并讨论了T(t)关于时间t的极限行为.

In this paper, we give the sufficient and necessary conditions for a general birth, death and catastrophe q - matrix Q generating a contraction integrated semigroup on l∞, and show that Q generates a minimal integrated Q- semigroup T（t） on l∞. A sufficient and necessary condition for T（t） to be monotone is also given. Finally, the Feller property of T（t） and its limit behaviour as time t tends to infinity are discussed.