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Fluctuations and moderate deviations for the mean fields of Hawkes processes
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The Hawkes process is a counting process that has self- and mutually-exciting features with many applications in various fields. In recent years, there have been many interests in the mean-field results of the Hawkes process and its extensions. It is known that the mean-field limit of a multivariate nonlinear Hawkes process is a time-inhomogeneous Poisson process. In this paper, we study the fluctuations for the mean fields and the large deviations associated with the fluctuations, i.e., the moderate deviations.
Forward citations
Cited by 3 Pith papers
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Scaling Limit Theorems for Multivariate Hawkes Processes and Stochastic Volterra Equations with Measure Kernel
Asymptotically critical multivariate Hawkes processes converge to the unique weak solution of a stochastic Volterra equation with a measure kernel, characterized by an admissible pair (K, Φ).
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Mean-Field Limits for Nearly Unstable Hawkes Processes
Nearly unstable Hawkes processes rescale to affine stochastic Volterra diffusions, and mean-field Hawkes systems exhibit synchronization, conditional independence, or extinction depending on n(1-||phi^n||)^2.
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Loglinear Hawkes processes
The paper proves explosion and nonexplosion criteria for exponential-transform Hawkes processes and establishes stability for nonpositive memory functions.
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