Nonhomogeneous Hawkes processes converge in the near-unstable regime to a family of generalized Feller random measures parameterized by a locally finite measure and a geometrically infinitely divisible distribution.
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Convergence of nonhomogeneous Hawkes processes and Feller random measures
Nonhomogeneous Hawkes processes converge in the near-unstable regime to a family of generalized Feller random measures parameterized by a locally finite measure and a geometrically infinitely divisible distribution.