An infinite-times renewal equation - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

An infinite-times renewal equation

Abstract

In neuroscience, the time elapsed since the last discharge has been used to predict the probability of the next discharge. Such predictions can be improved taking into account the last two discharge times, and possibly more. Such multi-time processes arise in many other areas and there is no universal limitation on the number of times to be used. This observation leads us to study the infinite-times renewal equation as a simple model to understand the meaning and properties of such partial differential equations depending on an infinite number of variables. We define two notions of solutions, prove existence and uniqueness of solutions, possibly measures. We also prove the long time convergence, with exponential rate, to the steady state in different, strong or weak, topologies depending on assumptions on the coefficients.
Fichier principal
Vignette du fichier
Infinite_times.pdf (373.43 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04056973 , version 1 (03-04-2023)

Identifiers

Cite

Xu'An Dou, Benoît Perthame, Chenjiayue Qi, Delphine Salort, Zhennan Zhou. An infinite-times renewal equation. 2023. ⟨hal-04056973⟩
87 View
74 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More