{"ID":2823085,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.01189","arxiv_id":"2601.01189","title":"Central limit theorem for a partially observed interacting system of Hawkes processes I: subcritical case","abstract":"We consider a system of $N$ Hawkes processes and observe the actions of a subpopulation of size $K \\le N$ up to time $t$, where $K$ is large. The influence relationships between each pair of individuals are modeled by i.i.d.Bernoulli($p$) random variables, where $p \\in [0,1]$ is an unknown parameter. Each individual acts at a {\\it baseline} rate $μ\u003e 0$ and, additionally, at an {\\it excitation} rate of the form $N^{-1} \\sum_{j=1}^{N} θ_{ij} \\int_{0}^{t} φ(t-s)\\,dZ_s^{j,N}$, which depends on the past actions of all individuals that influence it, scaled by $N^{-1}$ (i.e. the mean-field type), with the influence of older actions discounted through a memory kernel $φ\\colon \\mathbb{R}{+} \\to \\mathbb{R}{+}$. Here, $μ$ and $φ$ are treated as nuisance parameters. The aim of this paper is to establish a central limit theorem for the estimator of $p$ proposed in \\cite{D}, under the subcritical condition $Λp \u003c 1$.","short_abstract":"We consider a system of $N$ Hawkes processes and observe the actions of a subpopulation of size $K \\le N$ up to time $t$, where $K$ is large. The influence relationships between each pair of individuals are modeled by i.i.d.Bernoulli($p$) random variables, where $p \\in [0,1]$ is an unknown parameter. Each individual ac...","url_abs":"https://arxiv.org/abs/2601.01189","url_pdf":"https://arxiv.org/pdf/2601.01189v1","authors":"[\"Chenguang Liu\",\"Liping Xu\",\"An Zhang\"]","published":"2026-01-03T14:05:53Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\",\"q-fin.MF\"]","methods":"[]","has_code":false}