A note on the conditional probabilities of the telegraph process

Fabrizio Cinque

Statistics & Probability Letters, 2022, vol. 185, issue C

Abstract: We consider the telegraph process with two velocities, a1>a2∈R, and two rates of reversal, λ1,λ2>0. We study some of its features with respect to the conditional probability measure where both the initial speed and the number of changes of direction are known. We exhibit a new proof by induction of the (conditional) probability law and a detailed study of the distribution of the motion at time t>0 conditioned on its position at a previous time 00, its maximum and its minimum up to that moment.

Keywords: Telegraph process; Stochastic motions with drift; Distribution of maximum and minimum; Induction principle; Reflection principle (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2022.109431

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