On the distribution of the telegraph meander and its properties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915554358460416 |
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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 |