论文标题
电报过程中的一些结果受两个非标准边界的限制
Some results on the telegraph process confined by two non-standard boundaries
论文作者
论文摘要
我们分析了一个由两个边界限制的一维电报随机过程，分别是0和$ h> 0 $。该过程在边界处经历艰苦的反射（随机切换到完全吸收）。也就是说，当该过程撞击原点（阈值$ h $）时，它被吸收，概率$α$，或者以$ 1-α$的概率向上反射（向下反射），价格为$ 0 <α<1 $。我们就更新周期和吸收时间的预期值提供了各种结果。所采用的方法基于通过线性边界对合适复合泊松过程的第一个跨时间的分析。我们的分析还包括在经典KAC的缩放条件下获得的相应电报过程的合适停止时间与相应的扩散过程之间的一些比较。
We analyze the one-dimensional telegraph random process confined by two boundaries, 0 and $H>0$. The process experiences hard reflection at the boundaries (with random switching to full absorption). Namely, when the process hits the origin (the threshold $H$) it is either absorbed, with probability $α$, or reflected upwards (downwards), with probability $1-α$, for $0<α<1$. We provide various results on the expected values of the renewal cycles and of the absorption time. The adopted approach is based on the analysis of the first-crossing times of a suitable compound Poisson process through linear boundaries. Our analysis includes also some comparisons between suitable stopping times of the considered telegraph process and of the corresponding diffusion process obtained under the classical Kac's scaling conditions.
