Regenerative processes in the infinite mean cycle case
Regenerative processes in the infinite mean cycle case
复制标题
无限平均循环情况下的再生过程
DOI：
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发表时间：
2001
影响因子：
1
通讯作者：
N. Yanev
中科院分区：
文献类型：
--
作者：
K. Mitov;N. Yanev
考虑了一类非负交替再生过程，该过程在零随机时间（等待期）停留，然后跳到一个随机正水平，并在某个随机时间（生命期）后到达零，这取决于过程的演化.假设等待时间和生存期属于参数在区间（1/2，1]内的稳定律的吸引域.利用相应的交替更新过程的时间分布，得到了再生过程的分布函数的积分表示。给出了该过程在再生循环中的渐近性态，证明了不同类型的极限分布，应用了相应更新过程的一些新结果和关于分布收敛的两个极限定理.
A class of non-negative alternating regenerative processes is considered, where the process stays at zero random time (waiting period), then it jumps to a random positive level and hits zero after some random period (life period), depending on the evolution of the process. It is assumed that the waiting time and the lifetime belong to the domain of attraction of stable laws with parameters in the interval (½,1]. An integral representation for the distribution functions of the regenerative process is obtained, using the spent time distributions of the corresponding alternating renewal process. Given the asymptotic behaviour of the process in the regenerative cycle, different types of limiting distributions are proved, applying some new results for the corresponding renewal process and two limit theorems for the convergence in distribution.