Mean-field limits for non-linear Hawkes processes with excitation and inhibition

被引:5
|
作者
Pfaffelhuber, P. [1 ]
Rotter, S. [1 ]
Stiefel, J. [1 ]
机构
[1] Albert Ludwigs Univ Freiburg, Freiburg, Germany
关键词
Multivariate Hawkes process; Volterra equation; Spike train; DYNAMICS; BALANCE; STABILITY; MODELS;
D O I
10.1016/j.spa.2022.07.006
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We study a multivariate, non-linear Hawkes process Z(N) on the complete graph with N nodes. Each vertex is either excitatory (probability p) or inhibitory (probability 1 - p). We take the mean-field limit of Z(N), leading to a multivariate point process Z & macr;. If p&NOTEQUexpressionL;1/2, we rescale the interaction intensity by N and find that the limit intensity process solves a deterministic convolution equation and all components of Z & macr; are independent. In the critical case, p = 1/2, we rescale by N-1/2 and obtain a limit intensity, which solves a stochastic convolution equation and all components of Z & macr; are conditionally independent. (C) 2022 Elsevier B.V. All rights reserved.
引用
收藏
页码:57 / 78
页数:22
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