Mean-field limits for non-linear Hawkes processes with inhibition on a Erd\H{o}s-R\'{e}nyi-graph
| Autor: | Stiefel, Jakob |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study a multivariate, non-linear Hawkes process $Z^N$ on a $q$-Erd\H{o}s-R\'{e}nyi-graph with $N$ nodes. Each vertex is either excitatory (probability $p$) or inhibitory (probability $1-p$). If $p\neq\tfrac12$, we take the mean-field limit of $Z^N$, leading to a multivariate point process $\bar Z$. We rescale the interaction intensity by $N$ and find that the limit intensity process solves a deterministic convolution equation and all components of $\bar Z$ are independent. The fluctuations around the mean field limit converge to the solution of a stochastic convolution equation. In the critical case, $p=\tfrac12$, we rescale by $N^{1/2}$ and discuss difficulties, both heuristically and numerically. Comment: arXiv admin note: text overlap with arXiv:2102.01052 |
| Databáze: | arXiv |
| Externí odkaz: |
|