Bounds of random star discrepancy for HSFC-based sampling
This paper is dedicated to the estimation of the probabilistic upper bounds of star discrepancy for Hilbert's space filling curve (HSFC) sampling. The primary concept revolves around the stratified random sampling method, with the relaxation of the stringent requirement for a sampling number $...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025255 |
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| author | Xiaoda Xu |
| author_facet | Xiaoda Xu |
| author_sort | Xiaoda Xu |
| collection | DOAJ |
| description | This paper is dedicated to the estimation of the probabilistic upper bounds of star discrepancy for Hilbert's space filling curve (HSFC) sampling. The primary concept revolves around the stratified random sampling method, with the relaxation of the stringent requirement for a sampling number $ N = m^d $ in jittered sampling. We leverage the benefits of this sampling method to achieve superior results compared to Monte Carlo (MC) sampling. We also provide applications of the main result, which pertain to weighted star discrepancy, $ L_2 $-discrepancy, integration approximation in certain function spaces and examples in finance. |
| format | Article |
| id | doaj-art-ad604fdc86d94daeb9b1c75a0b87d47b |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-ad604fdc86d94daeb9b1c75a0b87d47b2025-08-20T02:26:19ZengAIMS PressAIMS Mathematics2473-69882025-03-011035532555110.3934/math.2025255Bounds of random star discrepancy for HSFC-based samplingXiaoda Xu0School of Mathematics and Science, Suqian University, Suqian 223800, ChinaThis paper is dedicated to the estimation of the probabilistic upper bounds of star discrepancy for Hilbert's space filling curve (HSFC) sampling. The primary concept revolves around the stratified random sampling method, with the relaxation of the stringent requirement for a sampling number $ N = m^d $ in jittered sampling. We leverage the benefits of this sampling method to achieve superior results compared to Monte Carlo (MC) sampling. We also provide applications of the main result, which pertain to weighted star discrepancy, $ L_2 $-discrepancy, integration approximation in certain function spaces and examples in finance.https://www.aimspress.com/article/doi/10.3934/math.2025255star discrepancystratified sampling$ \delta $-covershsfc samplingintegration approximation |
| spellingShingle | Xiaoda Xu Bounds of random star discrepancy for HSFC-based sampling AIMS Mathematics star discrepancy stratified sampling $ \delta $-covers hsfc sampling integration approximation |
| title | Bounds of random star discrepancy for HSFC-based sampling |
| title_full | Bounds of random star discrepancy for HSFC-based sampling |
| title_fullStr | Bounds of random star discrepancy for HSFC-based sampling |
| title_full_unstemmed | Bounds of random star discrepancy for HSFC-based sampling |
| title_short | Bounds of random star discrepancy for HSFC-based sampling |
| title_sort | bounds of random star discrepancy for hsfc based sampling |
| topic | star discrepancy stratified sampling $ \delta $-covers hsfc sampling integration approximation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025255 |
| work_keys_str_mv | AT xiaodaxu boundsofrandomstardiscrepancyforhsfcbasedsampling |