碰撞分支Q-矩阵生成的Markov积分半群(英文)

The Markov Integrated Semigroup Generated by the Collision Branching Q-matrix

首先证明了碰撞分支Q-矩阵在Banach空间l∞上能生成一个积分半群T(t),且当m1≤0时它的生成元是Q∞,当m1>0时它的生成元是Q0**.事实上,T(t)是一个Markov积分半群.然后论证了当m1>0时,T(t)满足Feller性质.

This paper aims to prove that the collision branching q-matrix can generate an integrated semigroup T（t） on L∞ and that if ml ≤ 0, its generator is Q∞ ; if ml 〉 0, its generator is Qo . In fact, T（t） is just a Markov integrated semigroup. Also, we obtain that if ml 〉 O, this integrated semigroup has the Feller property.