A Note on the Conditional Probabilities of the Telegraph Process

2022/02/03 by Cinque, Fabrizio
#60G50 #60K99 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2202.01904

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.

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