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

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. Zhytomyr State University, Zhytomyr, Ukraine

    A. A. Pogorui & T. Kolomiets

  2. Electrical and Computer Engineering, Tecnológico de Monterrey, Monterrey, México

    R. M. Rodríguez-Dagnino

Authors
  1. A. A. Pogorui
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  2. R. M. Rodríguez-Dagnino
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  3. T. Kolomiets
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Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 7, pp. 882–889, July, 2015.

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Pogorui, A.A., Rodríguez-Dagnino, R.M. & Kolomiets, T. The First Passage Time and Estimation of the Number of Level-Crossings for a Telegraph Process. Ukr Math J 67, 998–1007 (2015). https://doi.org/10.1007/s11253-015-1132-y

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  • DOI: https://doi.org/10.1007/s11253-015-1132-y

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