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Reflection principle for finite-velocity random motions. J Appl Probab 2022. [DOI: 10.1017/jpr.2022.58] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
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.
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A note on the conditional probabilities of the telegraph process. Stat Probab Lett 2022. [DOI: 10.1016/j.spl.2022.109431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Cinque F, Orsingher E. On the exact distributions of the maximum of the asymmetric telegraph process. Stoch Process Their Appl 2021. [DOI: 10.1016/j.spa.2021.09.011] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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