One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions
The law of the iterated logarithm (LIL), which describes the rate of convergence for a convergent lacunary series, was established by R. Salem and A. Zygmund. This rate is determined based on the variance-like term of the remainder after n terms of the series. In this article, we investigate a compa...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/8369711 |
| _version_ | 1827082272915849216 |
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| author | Santosh Ghimire |
| author_facet | Santosh Ghimire |
| author_sort | Santosh Ghimire |
| collection | DOAJ |
| description | The law of the iterated logarithm (LIL), which describes the rate of convergence for a convergent lacunary series, was established by R. Salem and A. Zygmund. This rate is determined based on the variance-like term of the remainder after n terms of the series. In this article, we investigate a comparable one-sided LIL for sums of signum functions, which also relies on the remainder after n terms. |
| first_indexed | 2024-03-11T21:35:36Z |
| format | Article |
| id | doaj.art-33ace03d4c674cd789274fcfa0f5d041 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2025-03-20T03:30:37Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-33ace03d4c674cd789274fcfa0f5d0412024-10-03T07:06:34ZengHindawi LimitedJournal of Mathematics2314-47852023-01-01202310.1155/2023/8369711One-Sided Version of Law of the Iterated Logarithm for Summations of Signum FunctionsSantosh Ghimire0Department of Applied Sciences and Chemical EngineeringThe law of the iterated logarithm (LIL), which describes the rate of convergence for a convergent lacunary series, was established by R. Salem and A. Zygmund. This rate is determined based on the variance-like term of the remainder after n terms of the series. In this article, we investigate a comparable one-sided LIL for sums of signum functions, which also relies on the remainder after n terms.http://dx.doi.org/10.1155/2023/8369711 |
| spellingShingle | Santosh Ghimire One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions Journal of Mathematics |
| title | One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions |
| title_full | One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions |
| title_fullStr | One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions |
| title_full_unstemmed | One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions |
| title_short | One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions |
| title_sort | one sided version of law of the iterated logarithm for summations of signum functions |
| url | http://dx.doi.org/10.1155/2023/8369711 |
| work_keys_str_mv | AT santoshghimire onesidedversionoflawoftheiteratedlogarithmforsummationsofsignumfunctions |