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[[en:seminaires:SeminaireMAV:index|Stochastics and Biology seminar]]\\
Wednesday June 10, 2026, 11AM, 16-26.209\\
**Aurélien Velleret**  //On the LAN and LAMN Properties for Mean-Field Model of Interacting Neurons//
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We study a mean-field system of interacting particles represented by stochastic differential equations (SDE's) with jumps, introduced in [1] as a model describing the time evolution of neuronal potentials in the human brain. Depending on the renormalization of the interaction : either averaging scaling (1/N) or diffusive scaling (1/\sqrt N)-it was shown in [1] and [2] that, as the number of particles tends to infinity, the system exhibit the propagation of chaos and conditional propagation of chaos, respectively. 
Assuming that the jump intensity depends on an unknown parameter, we establish the Local Asymptotic Normality (LAN) property in the averaging case and the Local Asymptotic Mixed Normality (LAMN) in the diffusive case. Some implications regarding the performance of the maximum likelihood estimator are also derived. 
The limiting Fisher information depends on the limit of the empirical measure of the system. It is deterministic in the averaging regime, random in diffusive regime. This phenomenon explains the dichotomy between LAN and LAMN. 
Based on joint works with Xavier Erny, Aline Duarte, Eva Löcherbach, Dasha Loukianova. 

[1] Fournier, N. and Löcherbach, E. (2016). On a toy model of interacting neurons. Ann.Inst. Henri Poincaré Probab. Stat. 52(4), 1844–1876. 
[2] Erny, X., Löcherbach, E. and Loukianova, D. (2021). Conditional propagation of chaos for mean field systems of interacting neurons. Electron. J. Probab. 26, 1–25.
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[[en:seminaires:SeminaireMAV:index|Stochastics and Biology seminar]]\\
Wednesday July 1, 2026, 11AM, 16-26.209\\
**Barbara Bricout** (LPSM (MAV)) //To be announced.//
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