Том 71
№ 10

All Issues

Kolomiets T.

Articles: 1
Article (English)

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   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 882-889

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.