Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences
This note contains a Chover-type Law of the k-Iterated Logarithm for weighted sums of strong mixing sequences of random variables with a distribution in the domain of a stable law. We show that the upper part of the LIL is similar to other studies in the literature; conversely, the lower half is sub...
| Main Author: | |
|---|---|
| Format: | Article |
| Published: |
Elsevier
2014
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/49234/ |
| _version_ | 1848797952123863040 |
|---|---|
| author | Trapani, Lorenzo |
| author_facet | Trapani, Lorenzo |
| author_sort | Trapani, Lorenzo |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This note contains a Chover-type Law of the k-Iterated Logarithm for weighted sums of strong mixing sequences of random variables with a distribution in the domain of a stable law. We show that the upper part of the LIL is similar to other studies in the literature; conversely, the lower half is substantially different. In particular, we show that, due to the failure of the classical version of the second Borel–Cantelli lemma, the upper and the lower bounds are separated, with the lower bound being further and further away as the memory of the sequence increases. |
| first_indexed | 2025-11-14T20:12:03Z |
| format | Article |
| id | nottingham-49234 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:12:03Z |
| publishDate | 2014 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-492342020-05-04T16:58:41Z https://eprints.nottingham.ac.uk/49234/ Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences Trapani, Lorenzo This note contains a Chover-type Law of the k-Iterated Logarithm for weighted sums of strong mixing sequences of random variables with a distribution in the domain of a stable law. We show that the upper part of the LIL is similar to other studies in the literature; conversely, the lower half is substantially different. In particular, we show that, due to the failure of the classical version of the second Borel–Cantelli lemma, the upper and the lower bounds are separated, with the lower bound being further and further away as the memory of the sequence increases. Elsevier 2014-12-15 Article PeerReviewed Trapani, Lorenzo (2014) Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences. Journal of Mathematical Analysis and Applications, 420 (2). pp. 908-916. ISSN 0022-247X Chover Law of the Iterated Logarithm; Strongly mixing sequence of random variables; Slowly varying function http://www.sciencedirect.com/science/article/pii/S0022247X14005897 doi:10.1016/j.jmaa.2014.06.042 doi:10.1016/j.jmaa.2014.06.042 |
| spellingShingle | Chover Law of the Iterated Logarithm; Strongly mixing sequence of random variables; Slowly varying function Trapani, Lorenzo Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences |
| title | Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences |
| title_full | Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences |
| title_fullStr | Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences |
| title_full_unstemmed | Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences |
| title_short | Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences |
| title_sort | chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences |
| topic | Chover Law of the Iterated Logarithm; Strongly mixing sequence of random variables; Slowly varying function |
| url | https://eprints.nottingham.ac.uk/49234/ https://eprints.nottingham.ac.uk/49234/ https://eprints.nottingham.ac.uk/49234/ |