Telegraph Processes

  • Shelemyahu Zacks
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2203)

Abstract

Telegraph processes are ON and OFF processes, which change intermittently, according to alternating renewal processes. In physics these processes describe the movement of a particle on a line. The following is a simple example from physics.

References

  1. Bshouty, D. Di Crescenzo, A. Martinucci, B. and Zacks, S. (2012) Generalized telegraph process with random delays, J. Appl. Prob., 49: 850–865.Google Scholar
  2. Di Crescenzo, A. Iuliano, A. Martinucci, B. and Zacks, S. (2013). Generalized telegraph process with random jumps. J. Appl. Prob., 50:450–463. Google Scholar
  3. Di Crescenzo, A. and Zacks, S.(2015). Probability law and flow function of Brownian motion driven by a generalized telegraph process. Method. Comput. Appl. Prob., 17:761–780. Google Scholar
  4. Stadje, W. and Zacks, S. (2003), Upper first-exit times of compound Poisson processes revisited. Prob. in Engr. and Inform. Sciences, 17:459–465.Google Scholar
  5. Stadje, W. and Zacks, S. (2004). Telegraph process with random velocities. J. Appl. Prob. 41:665–678. Google Scholar
  6. Xu, Y. De, S.K. and Zacks, S. (2015). Exact distribution of intermittently changing positive and negative compound Poisson process driven by an alternating renewal and related functions. Prob. in Engr. and Inform. Sciences, 29: 385–392. Google Scholar
  7. Zacks, S. (2004a). Generalized integrated telegraph processes and the distribution of related stopping times. J. Appl. Prob. 41:497–507. Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Shelemyahu Zacks
    • 1
  1. 1.Binghamton UniversityBinghamtonUSA

Personalised recommendations