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

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  • Pfaffelhuber, P.
  • Rotter, S.
  • Stiefel, J.

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.

Suggested Citation

  • Pfaffelhuber, P. & Rotter, S. & Stiefel, J., 2022. "Mean-field limits for non-linear Hawkes processes with excitation and inhibition," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 57-78.
    • Handle: RePEc:eee:spapps:v:153:y:2022:i:c:p:57-78
    DOI: 10.1016/j.spa.2022.07.006
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    References listed on IDEAS

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