AcademicArticleSCO_84957438159

abstract

• © 2015, Springer Science+Business Media New York. 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, ¿) for ¿ > 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.