单流出B型Q过程爆发后的存活时间分布

The Distribution of Lifetime of Q Process of B Type in Single Exit Case After Explosion

单流出B型Q过程是一类在理论和实际上很重要的Markov过程 ,它的Martin流出边界Be 是单点集 {b} .杨向群教授在文 [1]中 ,解决了单流出时B型Q过程的构造问题 .此类过程由一个行矢量α 0 ,常数C′或C′以及一个行协调解族 { η(λ) ,λ >0 }完全决定 .在文 [3]中 ,对有爆发的生灭过程 ,杨向群教授得到了生灭过程爆发后的存活时间分布、平均存活时间等许多性质 .在此基础上 ,在文 [4 ]中研究了单流出B型Q过程爆发后的期望停留与寿命 .我们对单流出B型Q过程进行了更深入的研究 ,得到了如下重要性质 ,这些性质都强烈地依赖于过程爆发后的构造 .①求出了过程爆发马上就灭亡的概率 .②求出了过程爆发后的存活时间分布 (Laplace变换形式 ) .③求出了过程寿命的分布以及经过流出点b的过程寿命的分布 (Laplace变换形式 )

The Q process of B type in single exit case is a very important kind of Markov process in theory and practice, its Martin exit boundary Be is a single-point set {b}. Professor Yang Xiangqun has constructed all Q process satisfying the backward equations in single exit case in document [1]. Such a process is defined by a row vector a≥0, constant C or C″, and a harmonic entrance family {η¯(λ),λ>0}. By studying the birth and death process, Professor Yang Xiangqun has followed some properties of the distribution of lifetime after explosion for this process, and calculated expected lifetime after explosion in document [3]. We study the expected staying and lifespan of Q process of B type in single exit case after explosion in [4]. In this article, author has made a further study of the properties of such process, which depends strongly on the construction of the process after the first explosion time. The main results are calculated as follows: 1 The probability of explosion which means the end of life. 2 The distribution of lifetime from explosion to the end of life (the Laplace transforms). 3 The distribution of lifespan and the distribution of lifespan on passing exit point b (the Laplace transforms).