论文标题
关于电报过程的最大分布
On the distribution of the maximum of the telegraph process
论文作者
论文摘要
在本文中，我们介绍了电报过程的最大值分布，在初始速度为正或均匀数和奇数速度逆转的情况下。对于具有正初始速度的电报过程，事实证明，反射原理是有效的，而在初始向左位移的情况下，条件分布受到从未访问半轴的正概率的扰动。 在上述四类最大条件分布之间建立了各种关系。 对于正面和负面的初始步骤及其限制行为，获得了电报过程最大值的无条件分布。此外，还提出了条件最大的累积分布和一般力矩。
In this paper we present the distribution of the maximum of the telegraph process in the cases where the initial velocity is positive or negative with an even and an odd number of velocity reversals. For the telegraph process with positive initial velocity a reflection principle is proved to be valid while in the case of an initial leftward displacement the conditional distributions are perturbed by a positive probability of never visiting the half positive axis. Various relationships are established among the mentioned four classes of conditional distributions of the maximum. The unconditional distributions of the maximum of the telegraph process are obtained for positive and negative initial steps as well as their limiting behaviour. Furthermore the cumulative distributions and the general moments of the conditional maximum are presented.
