The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian Sheets
A new class of Gaussian random fields is introduced in this article, described as additive Brownian sheets (ABSs), which can be regarded as a type of generalized Brownian sheet encompassing Brownian motions, Brownian sheets, and additive Brownian motions. The existence, joint continuity and the Höld...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/9/1425 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849312878644953088 |
|---|---|
| author | Mingjie Liang Chenfang Lin |
| author_facet | Mingjie Liang Chenfang Lin |
| author_sort | Mingjie Liang |
| collection | DOAJ |
| description | A new class of Gaussian random fields is introduced in this article, described as additive Brownian sheets (ABSs), which can be regarded as a type of generalized Brownian sheet encompassing Brownian motions, Brownian sheets, and additive Brownian motions. The existence, joint continuity and the Hölder law of the local times for ABSs are derived under certain conditions, and some results of the intersection local times for two independent Brownian sheets are also given as special cases. Furthermore, the intersection local times for two independent Brownian sheets in a Hida distribution is proved through white noise analysis, and the Wiener chaos expansion of the intersection local times is expressed in terms of <i>S</i>-transform. Additionally, the large deviations for the intersection local time of two independent Brownian sheets are established. The multi-parameter Gaussian random fields have become a core tool for complex system analysis due to their flexible multidimensional modeling capabilities. With the improvement of computational efficiency and interdisciplinary integration, the ABS constructed in this article will unleash greater potential in fields such as metaverse simulation, financial mathematics, climate science, precision medicine, quantum physics, and string theory. |
| format | Article |
| id | doaj-art-51cac44e7c474da0b918cacbb72964fe |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-51cac44e7c474da0b918cacbb72964fe2025-08-20T03:52:56ZengMDPI AGMathematics2227-73902025-04-01139142510.3390/math13091425The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian SheetsMingjie Liang0Chenfang Lin1School of Information Engineering, Sanming University, Sanming 365004, ChinaSchool of Education and Music, Sanming University, Sanming 365004, ChinaA new class of Gaussian random fields is introduced in this article, described as additive Brownian sheets (ABSs), which can be regarded as a type of generalized Brownian sheet encompassing Brownian motions, Brownian sheets, and additive Brownian motions. The existence, joint continuity and the Hölder law of the local times for ABSs are derived under certain conditions, and some results of the intersection local times for two independent Brownian sheets are also given as special cases. Furthermore, the intersection local times for two independent Brownian sheets in a Hida distribution is proved through white noise analysis, and the Wiener chaos expansion of the intersection local times is expressed in terms of <i>S</i>-transform. Additionally, the large deviations for the intersection local time of two independent Brownian sheets are established. The multi-parameter Gaussian random fields have become a core tool for complex system analysis due to their flexible multidimensional modeling capabilities. With the improvement of computational efficiency and interdisciplinary integration, the ABS constructed in this article will unleash greater potential in fields such as metaverse simulation, financial mathematics, climate science, precision medicine, quantum physics, and string theory.https://www.mdpi.com/2227-7390/13/9/1425additive Brownian sheetsintersection local timesHölder lawlarge deviations |
| spellingShingle | Mingjie Liang Chenfang Lin The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian Sheets Mathematics additive Brownian sheets intersection local times Hölder law large deviations |
| title | The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian Sheets |
| title_full | The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian Sheets |
| title_fullStr | The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian Sheets |
| title_full_unstemmed | The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian Sheets |
| title_short | The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian Sheets |
| title_sort | local times for additive brownian sheets and the intersection local times for independent brownian sheets |
| topic | additive Brownian sheets intersection local times Hölder law large deviations |
| url | https://www.mdpi.com/2227-7390/13/9/1425 |
| work_keys_str_mv | AT mingjieliang thelocaltimesforadditivebrowniansheetsandtheintersectionlocaltimesforindependentbrowniansheets AT chenfanglin thelocaltimesforadditivebrowniansheetsandtheintersectionlocaltimesforindependentbrowniansheets AT mingjieliang localtimesforadditivebrowniansheetsandtheintersectionlocaltimesforindependentbrowniansheets AT chenfanglin localtimesforadditivebrowniansheetsandtheintersectionlocaltimesforindependentbrowniansheets |