A Note on the Conditional Probabilities of the Telegraph Process

Fabrizio Cinque

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arXiv · 2202.01904

A Note on the Conditional Probabilities of the Telegraph Process

Fabrizio Cinque

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Abstract

We consider the telegraph process with two velocities, $a_1>a_2\in\mathbb{R}$, and two rates of reversal, $\lambda_1,\lambda_2>0$. 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 $0 0$, its maximum and its minimum up to that moment.

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Fabrizio Cinque. 2022-02-03. A Note on the Conditional Probabilities of the Telegraph Process. https://arxiv.org/abs/2202.01904

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