一类含瞬时态的Q-矩阵

A CLASS OF Q-MATRICES WITH INSTANTANEOUS STATES

设■其中0≤b_1<∞,0≤q_1<∞,i≥1。本文分别给出了Q为Q-矩阵及诚实Q-矩阵的充要条件,并证明了,如果Q是Q-矩阵,则存在无穷多个诚实Q-过程,对于含有限多个瞬时态的对角形Q-矩阵,也得到类似结果。本文所构造的Q-过程可以用其拉氏变换明显表达出来。

Let ■ where O≤b_i<∞, O≤q_i<∞, i≥1. In the present paper, some necessary and sufficient conditions for Q to be a Q-matrix or an honest Q-matrix are given respectively. Besides, it is proved that if Q is a Q-matrix, then there exist infinitely many Q-processes. Similar results for the diagonal Q-matrix with finite number of instantaneous states are derived. The processes constructed here can be explioitly represented by their Laplace transforms.