Strong limit of processes constructed from a renewal process
We construct a family of processes, from a renewal process, that have realizations that converge almost surely to the Brownian motion, uniformly on the unit time interval. Finally, we compute the rate of convergence in a particular case.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-10-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2023-0112 |
| _version_ | 1797646332251340800 |
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| author | Bardina Xavier Rovira Carles |
| author_facet | Bardina Xavier Rovira Carles |
| author_sort | Bardina Xavier |
| collection | DOAJ |
| description | We construct a family of processes, from a renewal process, that have realizations that converge almost surely to the Brownian motion, uniformly on the unit time interval. Finally, we compute the rate of convergence in a particular case. |
| first_indexed | 2024-03-11T15:00:04Z |
| format | Article |
| id | doaj.art-bde331528f5540c19c3ab0b68b8c0ac8 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-03-11T15:00:04Z |
| publishDate | 2023-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-bde331528f5540c19c3ab0b68b8c0ac82023-10-30T07:58:36ZengDe GruyterOpen Mathematics2391-54552023-10-0121149750910.1515/math-2023-0112Strong limit of processes constructed from a renewal processBardina Xavier0Rovira Carles1Department of Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, SpainFacultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, SpainWe construct a family of processes, from a renewal process, that have realizations that converge almost surely to the Brownian motion, uniformly on the unit time interval. Finally, we compute the rate of convergence in a particular case.https://doi.org/10.1515/math-2023-0112strong convergencerenewal processbrownian motion60f1760g15 |
| spellingShingle | Bardina Xavier Rovira Carles Strong limit of processes constructed from a renewal process Open Mathematics strong convergence renewal process brownian motion 60f17 60g15 |
| title | Strong limit of processes constructed from a renewal process |
| title_full | Strong limit of processes constructed from a renewal process |
| title_fullStr | Strong limit of processes constructed from a renewal process |
| title_full_unstemmed | Strong limit of processes constructed from a renewal process |
| title_short | Strong limit of processes constructed from a renewal process |
| title_sort | strong limit of processes constructed from a renewal process |
| topic | strong convergence renewal process brownian motion 60f17 60g15 |
| url | https://doi.org/10.1515/math-2023-0112 |
| work_keys_str_mv | AT bardinaxavier stronglimitofprocessesconstructedfromarenewalprocess AT roviracarles stronglimitofprocessesconstructedfromarenewalprocess |