论文标题
负反射原理和电报过程的联合分布及其最大
The Negative Reflection Principle and the Joint Distribution of the Telegraph Process and its Maximum
论文作者
论文摘要
在本文中，我们研究了电报过程的联合分布及其最大条件，以方向变化和初始速度的变化数量。我们证明，在阳性起步速度的情况下，反射原则的一种形式。我们称其为负反射原理，并将其推广到以恒定有限速度移动的随机运动的路径。在最后一节中，我们通过使用最大运动结果来获得电报过程的第一个通道时间的条件分布。最后，我们得出了第一个返回时间到原点的分布。
In this paper we study the joint distributions of the telegraph process and its maximum conditioned on the number of changes of direction and the initial velocity. We prove that in the case of positive starting velocity, a form of the reflection principle holds. We call it the negative reflection principle and we generalize it to the paths of the random motions moving with constant finite velocity. In the last section we obtain the conditional distribution of the first passage time of the telegraph process by using the known results on the maximum of the motion. Finally, we derive the distribution of the first returning time to the origin.
