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1 results

  • A Damped Telegraph Random Process with Logistic Stationary Distribution

  • Part of
  • Antonio Di Crescenzo, Barbara Martinucci
  • Journal:
    Journal of Applied Probability / Volume 47 / Issue 1 / March 2010
    Published online by Cambridge University Press:
    14 July 2016, pp. 84-96
    Print publication:
    March 2010
    • Article
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  • We introduce a stochastic process that describes a finite-velocity damped motion on the real line. Differently from the telegraph process, the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters. We obtain the probability law of the motion, which admits a logistic stationary limit in a special case. Various results on the distributions of the maximum of the process and of the first passage time through a constant boundary are also given.