2017
Том 69
№ 9

All Issues

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

Kolomiets T., Pogorui A. О., Rodriguez-Dagnino R. M.


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.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 7, pp 998-1007.

Citation Example: Kolomiets T., Pogorui A. О., Rodriguez-Dagnino R. M. The First Passage Time and Estimation of the Number of Level-Crossings for a Telegraph Process // Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 882-889.