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math.PR2025
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…
math.PR2024
Functional Limit Theorems for Hawkes Processes
Ulrich Horst, Wei Xu
We prove that the long-run behavior of Hawkes processes is fully determined by the average number and the dispersion of child events. For subcritical processes we provide FLLNs and…
math.PR2024
Path-dependent Fractional Volterra Equations and the Microstructure of Rough Volatility Models driven by Poisson Random Measures
Ulrich Horst, Wei Xu, Rouyi Zhang
We consider a microstructure foundation for rough volatility models driven by Poisson random measures. In our model the volatility is driven by self-exciting arrivals of market ord…