Wei Xu's Homepage
Personal Information
Occupation: （Tenure-track）Associate Professor
School：School of Mathematics and Statistics, Beijing Institute of Technology
Address: Wencui E413, Liangxiang, Fangshan, Beijing China
Email: xuwei.math@gmail.com
Research Interests
Random Fields and Stochastic Flows
Stochastic Volterra equations and their applications
Lévy processes and their local times & exponential functionals
Branching processes and interacting particle systems
09/2011 - 06/2014 Teaching Assistant Beijing Normal University, China
07/2013 - 08/2013 Visiting Student Bielefeld University, Germany
08/2014 - 09/2015 Exchange Student Cornell University, U.S.A.
07/2016 - 12/2016 Research Assistant Beijing Normal University, China
01/2017 - 03/2017 Visiting Scholar Concordia University, Canada
04/2017 - 09/2018 Postdoc Humboldt-Universität zu Berlin, Germany
10/2018 - 09/2020 Humboldt Research Fellowship Germany
10/2020 - 06/2023 Research assistant Humboldt-Universität zu Berlin, Germany
Ma, C., Wu, H. and Xu, W. (2025). (non-)Conditional limit theorems for Lévy processes. In preparation
Contreras, J. and Xu, W. (2024+). Branching structure in the local times of spectrally positive Lévy processes. In preparation
Denkert, R and Xu, W. (2024). Large deviations for marked Hawkes point measures. In coming
Preprints
Szymanski, G. and Xu, W. (2025). Mean-field limits for nearly unstable Hawkes processes. [Arxiv]
Horst, U., Xu, W. and Zhang, R. (2024). Path-dependent fractional Volterra equations and the microstructure of rough volatility models driven by Poisson random measures. [Arxiv]
Xu, W. (2024). Scaling limit theorems for multivariate Hawkes processes and stochastic Volterra equations with measure kernel. [Arxiv]
Xu, W. (2024). Stochastic Volterra equations for local times of spectrally positive Lévy processes with Gaussian components. [Arxiv]
Horst, U., Xu, W. and Zhang, R. (2023). Convergence of heavy-tailed Hawkes processes and the microstructure of rough volatility. [Arxiv] Submitted to Ann. Appl. Probab. (reversion submitted)
Horst, U. and Xu, W. (2025). Second-order regular variation and second-order approximation of Hawkes processes. To appear in J. Math. Anal. Appl. [Journal] [Arxiv] (It contains some auxilliary results that are used in Horst and Xu (2025, PTRF))
Horst, U. and Xu, W. (2025). Functional limit theorems for Hawkes processes. To appear in Probab. Theory Relat. Fields. [Journal] [Arxiv]
Xu, W. (2024). Stochastic Volterra equations for the local times of spectrally positive stable processes. Ann. Appl. Probab., 34 (3), 2733-2798. [Journal] [arXiv]
Xu, W. (2024). Diffusion approximations for marked self-excited systems with applications to general branching processes. Ann. Appl. Probab., 34 (3), 2650-2713. [Journal] [arXiv]
Xu, W. (2023). Asymptotics for exponential functionals of random walks. Stochastic Process. Appl., 165, 1-42. [Journal] [arXiv]
We appricate Zhihao Cui and Hao Wu for pointing out the following typos and errors:
(1) In the last line in Page 5: $\hat{\mathbf{P}}_x$ should be $\mathbf{P}_x$
(2) In Page 6, Line 10: The defintions of two transition functions should be switched !
(3) Remark 3.1 in Page 12 should be: Notice that $V$ and $\hat{V}$ are c\`adl\`ag, all the following claims still hold with $\tau_0^->n$, $\tau_0^+>n $, $V(x)$ and $\hat{V}(x)$ replaced by $L_n>0$, $M_n<0 $, $V(x-)$ and $\hat{V}(x-)$ respectively.
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]
Nonparametric/Parameter Estimation in Two-type CBI Processes,
11/02/2013 The Third Session of National Probability and Statistics Workshop for Young Scholars, Xuzhou China [Slides]
07/05/2014 Jilin University, Jilin China
Continuous-state Branching Processes in Random Environment Stochastic Equations with Jumps,
05/01/2016 Anhui Normal University, Anhui China
06/23/2016 Humboldt University in Berlin, Berlin Germany
Exponential Functionals of Levy processes with Light/Heavy Tails,
02/02/2017 Concordia University, Montréal Canada
26/08/2020 Bernoulli-IMS One World Symposium 2020, Online
Limit Order Books Driven by infinite-dimensional Hawkes Processes
04/20/2017 3rd Berlin-Princeton-Singapore Workshop on Quantitative Finance, Berlin Germany
07/05/2017 Workshop on BSDEs and SPDEs, Edingburg UK
15/03/2018 Concordia University, Montréal Canada
18/07/2018 10th World Congress of the Bachelier Finance Society , Dublin Ireland
Functional Limit Theorems for Marked Hawkes Point Measures,
08/07/2019 International Mathematical Statistics China, Dalian China
23/09/2019 Branching in Innsbruck, Innsbruck Austria
The Microstructure of Stochastic Volatility Models with Self-Exciting Jump Dynamics.
09/01/2020 Vienna University of Technology, Vienna Austria
27/09/2021 German Probability & Statistics Days Mannheim, Dreden Germany
05/06/2022 Humboldt University in Berlin, Berlin Germany
A Ray-Knight Theorem for Spectrally Positive Stable Processes.
22/09/2021 THU-PKU-BNU Joint Probability Webinar, Beijing China
27/09/2021 German Probability & Statistics Days Mannheim, Dreden Germany
06/10/2021 Fujian Normal University, Fuzhou China
01/05/2022 From Birth-Death Processes and Brownian Motions to Superprocesses, Xi'an China
18/10/2022 Seminario de Probabilidad para estudiantes, Mexico
Interplay of Hawkes Processes, General Branching Processes and Stable Local Time
13/10/2021 Jilin University, Changchun China
Functional Limit Theorems for Quasi-stationary Hawkes Processes
07/12/2022 Berlin Probability Colloquium, Berlin Germany
02/06/2023 Workshop on modelling with Hawkes processes: Theory, Statistics and Applications, Warsaw Poland
From Hawkes Stochastic Systems to Stochastic Volatility Models
21/03/2023 Beijing Institute of Technology, Beijing China [Slides]
06/09/2023 Nankai University, Tianjin China
Stochastic Volterra equations for the local times of spectrally positive stable processes