The local limit theorem for complex valued sequences: the parabolic case
We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in probability theory for random walks as well as in numerical a...
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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.685/ |
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| author | Coulombel, Jean-François Faye, Grégory |
| author_facet | Coulombel, Jean-François Faye, Grégory |
| author_sort | Coulombel, Jean-François |
| collection | DOAJ |
| description | We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in probability theory for random walks as well as in numerical analysis for studying the large time behavior of numerical schemes. |
| format | Article |
| id | doaj-art-3f56827bf25641b88a279ee7187222a5 |
| 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-3f56827bf25641b88a279ee7187222a52025-02-07T11:26:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G121801181810.5802/crmath.68510.5802/crmath.685The local limit theorem for complex valued sequences: the parabolic caseCoulombel, Jean-François0Faye, Grégory1Institut de Mathématiques de Toulouse – UMR 5219, Université de Toulouse, CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9 , FranceInstitut de Mathématiques de Toulouse – UMR 5219, Université de Toulouse, CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9 , FranceWe give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in probability theory for random walks as well as in numerical analysis for studying the large time behavior of numerical schemes.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.685/Convolutionasymptotic expansionstabilitylocal limit theorem |
| spellingShingle | Coulombel, Jean-François Faye, Grégory The local limit theorem for complex valued sequences: the parabolic case Comptes Rendus. Mathématique Convolution asymptotic expansion stability local limit theorem |
| title | The local limit theorem for complex valued sequences: the parabolic case |
| title_full | The local limit theorem for complex valued sequences: the parabolic case |
| title_fullStr | The local limit theorem for complex valued sequences: the parabolic case |
| title_full_unstemmed | The local limit theorem for complex valued sequences: the parabolic case |
| title_short | The local limit theorem for complex valued sequences: the parabolic case |
| title_sort | local limit theorem for complex valued sequences the parabolic case |
| topic | Convolution asymptotic expansion stability local limit theorem |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.685/ |
| work_keys_str_mv | AT coulombeljeanfrancois thelocallimittheoremforcomplexvaluedsequencestheparaboliccase AT fayegregory thelocallimittheoremforcomplexvaluedsequencestheparaboliccase AT coulombeljeanfrancois locallimittheoremforcomplexvaluedsequencestheparaboliccase AT fayegregory locallimittheoremforcomplexvaluedsequencestheparaboliccase |