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q-fin.MF2023★ 2 cited
Convergence of Heavy-Tailed Hawkes Processes and the Microstructure of Rough Volatility
Ulrich Horst, Wei Xu, Rouyi Zhang
We establish the weak convergence of the intensity of a nearly-unstable Hawkes process with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market…
math.PR2023
Second-Order Regular Variation and Second-Order Approximation of Hawkes Processes
Ulrich Horst, Wei Xu
This paper provides and extends second-order versions of several fundamental theorems on first-order regularly varying functions such as Karamata's theorem/representation and Taube…