Academic Journal
MULTIVARIATE HAWKES PROCESSES ON INHOMOGENEOUS RANDOM GRAPHS
| العنوان: | MULTIVARIATE HAWKES PROCESSES ON INHOMOGENEOUS RANDOM GRAPHS |
|---|---|
| المؤلفون: | Agathe-Nerine, Zoé |
| المساهمون: | Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques (INSMI-CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), ANR-19-CE40-0024,ChaMaNe,Enjeux mathématiques issus des neurosciences(2019) |
| المصدر: | ISSN: 0304-4149. |
| بيانات النشر: | HAL CCSD Elsevier |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Spatially extended system, Multivariate nonlinear Hawkes processes, Mean-field systems, Neural networks, Graph convergence, Random graph, 92B20, Graph convergence AMS Classification. 60F15, 60G55, 44A35, 60F15, 44A35,92B20, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] |
| الوصف: | International audience ; We consider a population of $N$ interacting neurons, represented by a multivariate Hawkes process: the firing rate of each neuron depends on the history of the connected neurons. Contrary to the mean-field framework where the interaction occurs on the complete graph, the connectivity between particles is given by a random possibly diluted and inhomogeneous graph where the probability of presence of each edge depends on the spatial position of its vertices. We address the well-posedness of this system and Law of Large Numbers results as $N\to\infty$. A crucial issue will be to understand how spatial inhomogeneity influences the large time behavior of the system. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/2106.12259; hal-03264303; https://hal.science/hal-03264303; https://hal.science/hal-03264303v2/document; https://hal.science/hal-03264303v2/file/spa_rev_hal.pdf; ARXIV: 2106.12259 |
| DOI: | 10.1016/j.spa.2022.06.019 |
| الاتاحة: | https://hal.science/hal-03264303 https://hal.science/hal-03264303v2/document https://hal.science/hal-03264303v2/file/spa_rev_hal.pdf https://doi.org/10.1016/j.spa.2022.06.019 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.A3587D34 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.spa.2022.06.019 |
|---|