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

P. Pfaffelhuber, S. Rotter and J. Stiefel

Stochastic Processes and their Applications, 2022, vol. 153, issue C, 57-78

Abstract: We study a multivariate, non-linear Hawkes process ZN 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 ZN, leading to a multivariate point process Z̄. If p≠12, we rescale the interaction intensity by N and find that the limit intensity process solves a deterministic convolution equation and all components of Z̄ are independent. In the critical case, p=12, we rescale by N1/2 and obtain a limit intensity, which solves a stochastic convolution equation and all components of Z̄ are conditionally independent.

Keywords: Multivariate Hawkes process; Volterra equation; Spike train (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2022.07.006

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