Wei Xu

If you can jump out from the time-dimension then randomness will not exist and the whole world is deterministic. All substances are crystal and light is the critical state, the main challenge for us comes from dimension restrictions. Thank GOD! We are not omnipotent and future is mysterious, relative randomness exists actually! Probability is meaningful! If tomorrow's stock prices can be known, I would lose my job! Time is unbelievable!

Now I am working with Prof. Horst to study Limit Order Books and other related problems (Supported by Alexander von Humboldt Foundation).

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.

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

Publications:

• 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

• Xu, W. (2021). Stochastic Volterra equations for the local times of spectrally positive stable processes. Submited to Ann. Appl. Probab., (first-round revision submitted) Arxiv e-print: 2105.02349

• Xu, W. (2021): Diffusion Approximations for Marked Self-excited Systems with Applications to General Branching Processes. Submited to Ann. Appl. Probab., (second-round revision submitted)  ArXiv e-print: 2101.01288

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