Preprints & Publications
Preprints
Horst, U. and Xu, W. (2024). Functional limit theorems for Hawkes processes. [Arxiv]
Horst, U., Xu, W. and Zhang, R. (2023). Convergence of heavy-tailed Hawkes processes and the microstructure of rough volatility. [Arxiv]
Horst, U. and Xu, W. (2023). Second-order regular variation and second-order approximation of Hawkes processes. [Arxiv]
Xu, W. (2023). Stochastic Volterra equations for the local times of spectrally positive Lévy processes with finite mean. In coming
Horst, U., Xu, W. and Zhang, R. (2023+). The microeconomic foundations of rough stochastic volatility with self-exciting sharp-rises. In coming
In progress
Denkert, R and Xu, W. (2023+). Large deviations for marked Hawkes point measures.
Publications
Xu, W. (2023+). Stochastic Volterra equations for the local times of spectrally positive stable processes. To appear in Ann. Appl. Probab. [arXiv]
Xu, W. (2023+). Diffusion approximations for marked self-excited systems with applications to general branching processes. To appear in Ann. Appl. Probab. [arXiv]
Xu, W. (2023). Asymptotics for exponential functionals of random walks. Stochastic Process. Appl., 165, 1-42. [Journal] [arXiv]
Horst, U. and Xu, W. (2022). The microstructure of stochastic volatility models with self-exciting jump dynamics. Ann. Appl. Probab., 32(6), 4568-4610. [Journal] [arXiv]
Xu, W. (2021). Asymptotic results for heavy-tailed Lévy processes and their exponential functionals. Bernoulli, 27(4), 2766–2803. [Journal] [arXiv]
Horst, U. and Xu, W. (2021). Functional limit theorems for marked Hawkes point measures. Stochastic Process. Appl., 134, 94-131. [Journal] [arXiv]
Horst, U. and Xu, W. (2019). A scaling limit for limit order books driven by Hawkes processes. SIAM J. Finan. Math., 10(2), 350–393. [Journal] [arXiv]
Li, Z. and Xu, W. (2018). Asymptotic results for exponential functionals of Lévy processes. Stochastic Process. Appl., 128, 108–131. [Journal] [arXiv]
He, H., Li, Z. and Xu, W. (2018). Continuous-state Branching Processes in Lévy Random Environments. J. Theoret. Probab., 31, 1-23. [Journal] [arXiv]
Xu, W. (2016). Backward doubly stochastic equations with jumps and comparison theorems. J. Math. Anal. Appl., 443(1), 596-624. [Journal] [arXiv]
Xu, W. (2014). Parameter estimation in two-type continuous-state branching processes with immigration. Stat. Probab. Lett., 91, 124-134. [Journal] [arXiv]