THE FIRST PASSAGE TIME AND ESTIMATION OF THE NUMBER OF LEVEL-CROSSINGS FOR A TELEGRAPH PROCESS

被引：7
|
作者：
Pogorui, A. A. [1 ]
Rodriguez-Dagnino, R. M. [2 ]
Kolomiets, T. [1 ]
机构：
[1] Zhytomyr State Univ, Zhytomyr, Ukraine
[2] Tecnol Monterrey, Elect & Comp Engn, Monterrey, Mexico
来源：
UKRAINIAN MATHEMATICAL JOURNAL | 2015年 / 67卷 / 07期
关键词：
Passage Time; Sample Path; Wiener Process; Interarrival Time; Hydrodynamic Limit;
D O I：
10.1007/s11253-015-1132-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is a well-known result that almost all sample paths of a Brownian motion or Wiener process {W(t)} have infinitely many zero-crossings in the interval (0, delta) for delta > 0. Under the Kac condition, the telegraph process weakly converges to the Wiener process. We estimate the number of intersections of a level or the number of level-crossings for the telegraph process. Passing to the limit under the Kac condition, we also obtain an estimate of the level-crossings for the Wiener process.
引用
收藏
页码：998 / 1007
页数：10
相关论文
共 50 条
12345