一般突变过程诱导的积分半群
An Integrated Semigroup Induced by the General Catastrophe Process
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摘要: 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.Abstract: 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.
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