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Reflection principle for finite-velocity random motions

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  15 December 2022

Fabrizio Cinque Open the ORCID record for Fabrizio Cinque [Opens in a new window]
Fabrizio Cinque*
Affiliation:
Sapienza University of Rome
*
*Postal address: Department of Statistical Sciences, Sapienza University of Rome, Italy. Email address: fabrizio.cinque@uniroma1.it
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Abstract

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.

Keywords

Reflection principletelegraph processrandom walksdistribution of the maximuminduction principle

MSC classification

Primary: 60G17: Sample path properties
Secondary: 60K99: None of the above, but in this section
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 2 , June 2023 , pp. 479 - 492
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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