On the distribution of the telegraph meander and its properties

Fuente: arXiv
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Autori principali: Pedicone, Andrea, Orsingher, Enzo
Natura: Preprint
Pubblicazione: 2025
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author Pedicone, Andrea
Orsingher, Enzo
author_facet Pedicone, Andrea
Orsingher, Enzo
contents In this paper we present the distribution of the telegraph meander, a random function obtained by conditioning the telegraph process to stay above the zero level. The reflection principle for finite-velocity random motions allows the law of the telegraph meander to be expressed in terms of the spatial derivative of the law of the telegraph process with initial negative velocity. As a result, we are able to obtain the characteristic function, the moments and the hyperbolic equation that governs the law of the telegraph meander. Furthermore, we prove that Brownian meander is the weak limit of the telegraph meander.
format Preprint
id arxiv_https___arxiv_org_abs_2504_11387
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the distribution of the telegraph meander and its properties
Pedicone, Andrea
Orsingher, Enzo
Probability
Primary 60K99, Secondary 60F17
In this paper we present the distribution of the telegraph meander, a random function obtained by conditioning the telegraph process to stay above the zero level. The reflection principle for finite-velocity random motions allows the law of the telegraph meander to be expressed in terms of the spatial derivative of the law of the telegraph process with initial negative velocity. As a result, we are able to obtain the characteristic function, the moments and the hyperbolic equation that governs the law of the telegraph meander. Furthermore, we prove that Brownian meander is the weak limit of the telegraph meander.
title On the distribution of the telegraph meander and its properties
topic Probability
Primary 60K99, Secondary 60F17
url https://arxiv.org/abs/2504.11387