Wei Xu, Prof. Dr.

I am an (tenure-track) associated professor at School of Mathematics and Statistics, Beijing Institute of Technology, July 2023. 

From April, 2017 to Sep, 2020, I was a postdoctoral researcher (Supported by Alexander von Humboldt Foundation) in Department of Mathematics, Humboldt-Universität zu Berlin. From Oct, 2020 to June, 2023, I was a research assistent in Department of Mathematics, Humboldt-Universität zu Berlin. 

Please visit my ResearchGate and Google sites.

Short CV:

• 09/2007---06/2011 B.S. Statistics and Actuarial Sciences, School of Mathematics, Jilin University, P.R.C.
• 09/2011---06/2013 M.S. Probability and Statistics, School of Mathematical Sciences, Beijing Normal University, P.R.C. 
• 08/2014---09/2015 Exchange graduate student, School of Operation Research and Information Engineering, Cornell University, U.S.A.
• 09/2013---06/2016 Ph.D. Probability and Statistics, School of Mathematical Sciences, Beijing Normal University, P.R.C.

Academic Appointments

• 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

Major Research Interests:

• Interacting particle system and Limit order book modelling
• Affine processes and Term-structure of interest rate
• (General) Continuous-state Braching processes in determinstic/random envionment and Stochastic equations
• Exponential functionals of Levy processes and their applicaitons
• Statistical inference of stochastic processes with light/heavy-tails
• Backward doubly stochastic differential equaitons with jumps and their applications

Preprints:

• Horst, U. and Xu, W. (2023). Second-order regular variation and second-order approximation of Hawkes processes. Arxiv e-print: 2311.02655

Publications:

• Xu, W. (2023). Stochastic Volterra equations for the local times of spectrally positive stable processes. To appear in Ann. Appl. Probab. Arxiv e-print: 2105.02349

• Xu, W. (2023): Diffusion Approximations for Marked Self-excited Systems with Applications to General Branching Processes. To appear in Ann. Appl. Probab. ArXiv e-print: 2101.01288

• Xu, W. (2023+). Asymptotics for Exponential Functionals of Random Walks. To appear in Stochastic Process. Appl., Arxiv e-print: 2201.02975

• Horst, U. and Xu, W. (2022): The Microstructure of Stochastic Volatility Models with Self-Exciting Jump Dynamics.  Ann. Appl. Probab., 32 (6), 4568-4610. ArXiv e-print: 1911.12969

• Xu, W. (2021): Asymptotic Results for Heavy-tailed Lévy Processes and their Exponential Functionals.Bernoulli 27(4), 2766–2803, ArXiv e-print: 1912.04795

• Horst, U. and Xu, W. (2019): Functional Limit Theorems for Marked Hawkes Point Measures. Stochastic Process. Appl. 134, 94-131. ArXiv e-print: 1908.06703

• 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. ArXiv e-print: 1709.01292   

• Xu, W. (2018): Crump-Mode-Jagers Processes with Immigration and Their Scaling Limits: Light-tailed Case. ArXiv e-print: 1809.05931.

• Li, Z. and Xu, W. (2018): Asymptotic Results for Exponential Functionals of Levy Processes. Stochastic Process. Appl.128, 108–131 .

• He, H., Li, Z. and Xu, W. (2017): Continuous-state Branching Processes in Levy Random Environments. Journal of Theoretical Probability, 1-23.

• Xu, W. (2016). Backward doubly stochastic equations with jumps and comparison theorems. Journal of Mathematical Analysis and Applications, 443(1), 596-624.

• Xu, W. (2014): Parameter Estimation in Two-type Continuous-state Branching Processes with Immigration. Statististics and Probability Letters, 91, 124-134.

Preprints:

• Xu, W. (2021). Asymptotic Results for Rough Continuous-state Branching Processes. (An supplement article) Arxiv e-print:2107.05888

Selected Presentations:

• 11/02/2013 Parameter Estimation in Two-type CBI Processes, The Third Session of National Probability and Statistics Workshop for Young Scholars, Xuzhou China

• 07/05/2014 Nonparametric Estimation in CBI Processes. Jilin University, Jilin China

• 05/01/2016 Survival Probability of Continuous-state Branching Processes in Random Environment, Anhui Normal University, Anhui China

• 06/23/2016 Continuous-state Branching Processes in Random Environment Stochastic Equations with Jumps, Humboldt University in Berlin, Berlin Germany

• 02/02/2017 Exponential Functionals of Levy processes with Light/Heavy Tails, Concordia University, Montréal Canada

• 04/20/2017 Limit Order Books Driven by infinite-dimensional Hawkes Processes, 3rd Berlin-Princeton-Singapore Workshop on Quantitative Finance, Berlin Germany

• 07/05/2017 A Scaling Limit for LOBs Driven by infinite-dimensional Hawkes Processes. Workshop on BSDEs and SPDEs, Edingburg UK.

• 15/03/2018 Limit Order Books, Hawkes Processes and Particle Systems. Concordia University, Montréal Canada

• 18/07/2018 A Scaling Limit for Limit Order Books Driven by Hawkes Processes. 10th World Congress of the Bachelier Finance Society , Dublin Ireland

• 08/07/2019 Diffusion Approximation for CMJ-Processes. International Mathematical Statistics China, Dalian China

• 23/09/2019 Functional Limit Theorems for Marked Hawkes Point Measures, 2019 Branching in Innsbruck, Innsbruck Austria

• 09/01/2020 The Microstructure of Stochastic Volatility Models with Self-Exciting Jump Dynamics. Vienna University of Technology, Vienna Austria