Rough Paths above Weierstrass Functions
Rough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. The fundamental observation of rough paths theory is that if one can define “iterated integrals” above a signal, then one can construct solutions to differential equations drive...
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| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.635/ |
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| author | Cellarosi, Francesco Selk, Zachary |
| author_facet | Cellarosi, Francesco Selk, Zachary |
| author_sort | Cellarosi, Francesco |
| collection | DOAJ |
| description | Rough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. The fundamental observation of rough paths theory is that if one can define “iterated integrals” above a signal, then one can construct solutions to differential equations driven by the signal.The typical examples of the signals of interest are stochastic processes such as (fractional) Brownian motion. However, rough paths theory is not inherently random and therefore can treat irregular deterministic driving signals such as a (vector-valued) Weierstrass function. This note supplies a construction of a rough path above vector-valued Weierstrass functions. |
| format | Article |
| id | doaj-art-3c4214e4b9024df48943401caf494ca5 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-3c4214e4b9024df48943401caf494ca52025-02-07T11:26:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G121555157010.5802/crmath.63510.5802/crmath.635Rough Paths above Weierstrass FunctionsCellarosi, Francesco0Selk, Zachary1Department of Mathematics and Statistics, Queen’s University, CanadaDepartment of Mathematics and Statistics, Queen’s University, CanadaRough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. The fundamental observation of rough paths theory is that if one can define “iterated integrals” above a signal, then one can construct solutions to differential equations driven by the signal.The typical examples of the signals of interest are stochastic processes such as (fractional) Brownian motion. However, rough paths theory is not inherently random and therefore can treat irregular deterministic driving signals such as a (vector-valued) Weierstrass function. This note supplies a construction of a rough path above vector-valued Weierstrass functions.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.635/Rough pathsWeierstrass functions |
| spellingShingle | Cellarosi, Francesco Selk, Zachary Rough Paths above Weierstrass Functions Comptes Rendus. Mathématique Rough paths Weierstrass functions |
| title | Rough Paths above Weierstrass Functions |
| title_full | Rough Paths above Weierstrass Functions |
| title_fullStr | Rough Paths above Weierstrass Functions |
| title_full_unstemmed | Rough Paths above Weierstrass Functions |
| title_short | Rough Paths above Weierstrass Functions |
| title_sort | rough paths above weierstrass functions |
| topic | Rough paths Weierstrass functions |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.635/ |
| work_keys_str_mv | AT cellarosifrancesco roughpathsaboveweierstrassfunctions AT selkzachary roughpathsaboveweierstrassfunctions |