Academic Journal
Local limit theorems for complex valued sequences: Old & New
| Title: | Local limit theorems for complex valued sequences: Old & New |
|---|---|
| Authors: | Coulombel, Jean-François, Faye, Grégory |
| Contributors: | Faye, Grégory, Centre Mersenne, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), ANR-24-CE40-3260,HEAD,Évolutions hyperboliques, asymptotiques et dynamique(2024), ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), ANR-21-CE40-0008,Indyana,Dynamiques d'invasion et asymptotiques non triviales(2021) |
| Source: | Journées équations aux dérivées partielles. :1-15 |
| Publisher Information: | Cellule MathDoc/Centre Mersenne, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Description: | In probability theory, local limit theorems provide an asymptotic expansion of the convolution powers of a probability distribution supported on ℤ with uniform bounds on the remainders. In this review, we present some recent results for the iterated convolution of complex valued integrable sequences in one space dimension. In the so-called parabolic case, we give a complete expansion, at any accuracy order, for these convolution powers and we provide sharp, pointwise, generalized Gaussian bounds for the remainders. We also present an extension of our main result to the semi-discrete setting (time-continuous convolution problems), and discuss several natural perspectives. |
| Document Type: | Article Conference object Report |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 2118-9366 |
| DOI: | 10.5802/jedp.686 |
| Access URL: | https://hal.science/hal-04802742v1 https://doi.org/10.5802/jedp.686 https://hal.science/hal-04802742v1/document |
| Accession Number: | edsair.doi.dedup.....e4ee3c5c94e0a44d433ea92aa89415cc |
| Database: | OpenAIRE |
| ISSN: | 21189366 |
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| DOI: | 10.5802/jedp.686 |