We propose a continuous-time adaptation of the well-known concept of success runs by considering a marked point process with two types of marks (success-failure) that appear according to an appropriate continuous-time Markov chain. By constructing a bivariate imbedded process (consisting of a run-counting and a phase process), we offer recursive formulas and generating functions for the distribution of the number of runs and the waiting time until the appearance of the n-th success run. We investigate the three most popular counting schemes: (i) overlapping runs of length k, (ii) non-overlapping runs of length k and (iii) runs of length at least k. We also present examples of applications regarding: the total penalty cost in a maintenance reliability system, the number of risky situations in a non-life insurance portfolio and the number of runs of increasing (or decreasing) asset price movements in high-frequency financial data.

中文翻译：

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连续时间马尔可夫链中成功运行次数的分布

我们通过考虑具有适当连续时间马尔可夫链出现的两种标记（成功失败）的标记点过程，提出对成功运行的著名概念的连续时间适应。通过构造双变量嵌入过程（由运行计数和阶段过程组成），我们提供了递归公式，并生成了用于分配运行次数和等待时间直到第n次成功运行的分布的函数。我们研究了三种最流行的计数方案：（I）重叠的长度的游程ķ，（ⅱ）非重叠长度的游程ķ至少和（iii）长度的游程ķ。我们还提供以下应用示例：维护可靠性系统中的总罚款成本，非人寿保险投资组合中的风险情况数量以及高频金融数据中资产价格波动的运行次数（增加或减少） 。