The First Passage Time and Estimation of the Number of Level-Crossings for a Telegraph Process

  • T. Kolomiets
  • A. О. Pogorui Zhytomyr State Univ., Ukraine
  • R. M. Rodriguez-Dagnino Monterrey Inst. Technol., Mexico

Abstract

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, δ) for δ > 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.
Published
25.07.2015
How to Cite
KolomietsT., PogoruiA. О., and Rodriguez-DagninoR. M. “The First Passage Time and Estimation of the Number of Level-Crossings for a Telegraph Process”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 7, July 2015, pp. 882-9, http://umj.imath.kiev.ua/index.php/umj/article/view/2031.
Section
Research articles