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1 results

  • Reflection principle for finite-velocity random motions

  • Part of
  • Fabrizio Cinque
  • Journal:
    Journal of Applied Probability / Volume 60 / Issue 2 / June 2023
    Published online by Cambridge University Press:
    15 December 2022, pp. 479-492
    Print publication:
    June 2023
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  • We present a reflection principle for a wide class of symmetric random motions with finite velocities. We propose a deterministic argument which is then applied to trajectories of stochastic processes. In the case of symmetric correlated random walks and the symmetric telegraph process, we provide a probabilistic result recalling the classical reflection principle for Brownian motion, but where the initial velocity has a crucial role. In the case of the telegraph process we also present some consequences which lead to further reflection-type characteristics of the motion.