@article{Kolomiets_Pogorui_Rodriguez-Dagnino_2015, title={The First Passage Time and Estimation of the Number of Level-Crossings for a Telegraph Process}, volume={67}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2031}, abstractNote={It is a well-known result that almost all sample paths of a Brownian motion or Wiener process <em class="EmphasisTypeItalic ">{W</em>(<em class="EmphasisTypeItalic ">t</em>)<em class="EmphasisTypeItalic ">}</em> have infinitely many zero-crossings in the interval (0<em class="EmphasisTypeItalic ">, δ</em>) for <em class="EmphasisTypeItalic "> δ ></em&gt; 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.}, number={7}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Kolomiets, T. and PogoruiA. О. and Rodriguez-Dagnino, R. M.}, year={2015}, month={Jul.}, pages={882-889} }