HAWKES PROCESSES ON LARGE NETWORKS

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A weak solution theory for stochastic Volterra equations of convolution type (2019, methodology): “ity satisﬁes λt = g 0(t) + Z [0,t) K(t−s)dNs. 2 Various multivariate and nonlinear generalizations have also been studied and applied; see Br´emaud and Massouli´e (1996); Daley and Vere-Jones (2003); Delattre et al. (2016) and the references there. Solutions of (1.1) are neither semimartingales nor ”
Renewal in Hawkes processes with self-excitation and inhibition (2018, methodology): “ce of a latency period before the successive activations of a neuron. A large part of the literature on Hawkes processes for neurosciences uses large systems approximations by mean-ﬁeld limits (e.g., [7, 12, 11, 13]) or stabilization properties (e.g., [14] using Erlang kernels). Here, we consider a ”