Elephant Random Walk with a Random Step Size and Gradually Increasing Memory and Delays
The ERW model was introduced twenty years ago to study memory effects in a one-dimensional discrete-time random walk with a complete memory of its past throughout a parameter <i>p</i> between zero and one. Several variations of the ERW model have recently been introduced. In this work, w...
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MDPI AG
2024-09-01
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| author | Rafik Aguech |
| author_facet | Rafik Aguech |
| author_sort | Rafik Aguech |
| collection | DOAJ |
| description | The ERW model was introduced twenty years ago to study memory effects in a one-dimensional discrete-time random walk with a complete memory of its past throughout a parameter <i>p</i> between zero and one. Several variations of the ERW model have recently been introduced. In this work, we investigate the asymptotic normality of the ERW model with a random step size and gradually increasing memory and delays. In particular, we extend some recent results in this subject. |
| format | Article |
| id | doaj-art-5b6fc6fe27e4405c95dfad40c3f7c55c |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-5b6fc6fe27e4405c95dfad40c3f7c55c2025-08-20T01:56:10ZengMDPI AGAxioms2075-16802024-09-0113962910.3390/axioms13090629Elephant Random Walk with a Random Step Size and Gradually Increasing Memory and DelaysRafik Aguech0Department of Statistics and Operation Research, King Saud University, Riyadh 11451, Saudi ArabiaThe ERW model was introduced twenty years ago to study memory effects in a one-dimensional discrete-time random walk with a complete memory of its past throughout a parameter <i>p</i> between zero and one. Several variations of the ERW model have recently been introduced. In this work, we investigate the asymptotic normality of the ERW model with a random step size and gradually increasing memory and delays. In particular, we extend some recent results in this subject.https://www.mdpi.com/2075-1680/13/9/629elephant random walkcentral limit theoremasymptotic distributions for expressionsnormal distributionMittag-Leffler distributionphase transition |
| spellingShingle | Rafik Aguech Elephant Random Walk with a Random Step Size and Gradually Increasing Memory and Delays Axioms elephant random walk central limit theorem asymptotic distributions for expressions normal distribution Mittag-Leffler distribution phase transition |
| title | Elephant Random Walk with a Random Step Size and Gradually Increasing Memory and Delays |
| title_full | Elephant Random Walk with a Random Step Size and Gradually Increasing Memory and Delays |
| title_fullStr | Elephant Random Walk with a Random Step Size and Gradually Increasing Memory and Delays |
| title_full_unstemmed | Elephant Random Walk with a Random Step Size and Gradually Increasing Memory and Delays |
| title_short | Elephant Random Walk with a Random Step Size and Gradually Increasing Memory and Delays |
| title_sort | elephant random walk with a random step size and gradually increasing memory and delays |
| topic | elephant random walk central limit theorem asymptotic distributions for expressions normal distribution Mittag-Leffler distribution phase transition |
| url | https://www.mdpi.com/2075-1680/13/9/629 |
| work_keys_str_mv | AT rafikaguech elephantrandomwalkwitharandomstepsizeandgraduallyincreasingmemoryanddelays |