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

• Datum: 2015
• Hauptverfasser: Kolomiets, T., Pogorui, A. О., Rodriguez-Dagnino, R. M., Коломиєць, Т., Погоруй, А. О., Родріжес-Дагніно, Р.М.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2015
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/2031
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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 interse...