AI 中文总结
本文研究两类速度受随机试验驱动的广义电报过程，分别推导其概率律的离散分量及给定初始速度时条件概率律的绝对连续分量，还得到了相关计数过程第n次事件时间的条件分布。
AI 中文摘要
我们研究一种广义电报过程，其中速度由随机试验控制，具体考虑等待时间的分布。在该电报过程中，在计数过程出现到达时，实数线上运动的粒子可改变方向，此方向改变由随机试验的结果驱动。第一种情形中，随机试验独立同分布，等待时间服从Mittag-Leffler分布；第二种情形中，随机试验遵循Pólya urn方案，首次等待时间服从广义Mittag-Leffler分布，其余等待时间服从Mittag-Leffler分布。两种情形下，我们均得到其概率律的离散分量，还推导了给定初始速度时条件概率律的绝对连续分量，比较了不同参数下概率律绝对连续分量的图像，得到了与这些电报过程相关的计数过程第n次事件时间在给定初始速度条件下的分布。
英文摘要
We study a generalized telegraph process in which the velocity is governed by random trials by considering the specific distribution of waiting times. In this telegraph process, a particle moving on real line may change its direction whenever there is an arrival in a counting process. This direction change is driven by the outcomes of random trials. In the first case, random trials are independent and identically distributed, and waiting times have Mittag-Leffler distribution. In the second case, random trials follow Pólya urn scheme and the first waiting time is generalized Mittag-Leffler distributed whereas other waiting times have Mittag-Leffler distribution. In both cases, we obtain the discrete component of their probability law. Also, absolutely continuous components of their conditional probability law given initial velocity are derived. The plots of absolutely continuous components of their probability law are compared for different parameters. Conditional on the initial velocity, the distributions of $n$th event time of counting processes associated with these telegraph processes are obtained.
