Welcome to Xiong's Website

Research interests

I  am interested in probability theory and its applications, particularly in complex systems influenced by random factors. My current research focuses on the intersection of probability, statistics, partial differential equations (PDEs), and machine learning. I am particularly interested in applying theoretical insights from stochastic analysis and PDEs to solve challenging problems in machine learning and data-driven applications. My current work investigates inverse problems and machine learning within stochastic dynamic systems, especially interacting particle systems (IPS), aiming to establish solid mathematical foundations and develop efficient, scalable algorithms.

Publications and Preprints

1. Minimax rates for learning kernels in operators (With Sichong Zhang and Fei Lu), submitted.

2. Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel (With Quanjun Lang, Fei Lu and Mauro Maggioni), submitted.

3. Optimal minimax rate of learning interaction kernels (with Fei Lu and Inbar Seroussi), submitted.

4. Gaussian fluctuations for the wave equation under rough random perturbations (with Raluca M. Balan, Jingyu Huang, Panqiu Xia, and Wangjun Yuan), Stoch. Process. Their Appl 182 (2025) 104569.

5. Stochastic wave equation with additive fractional noise: solvability and global Hölder continuity (with Yaozhong Hu and Shuhui Liu), submitted.

6. Moment asymptotics for super-Brownian motions (with Yaozhong Hu, Panqiu Xia and Jiayu Zheng), Bernoulli 30(4): 3119-3136.

7. A Data-Adaptive Prior for Bayesian Learning of Kernels in Operators (with Neil K. Chada, Quanjun Lang and Fei Lu), Journal of Machine Learning Research 25 (2024) 1-37.

8. Necessary and sufficient conditions to solve parabolic Anderson model with rough noise  (with Yaozhong Hu and Shuhui Liu), Electron. J. Probab. 29: 1-48 (2024).

9. Nonlinear stochastic wave Equation driven by rough noise (with Yaozhong Hu and Shuhui Liu),  J. Differential Equations 331 (2022), 99–161.

10. Mean square stability of stochastic theta method for stochastic differential equations driven by fractional Brownian motion (with Yaozhong Hu, Chengming Huang and Min Li),  J. Comput. Appl. Math. 420 (2023), Paper No. 114804.

11. Intermittency properties for a large class of stochastic PDEs driven by fractional space-time noises (with Yaozhong Hu), Stoch. Partial Differ. Equ. Anal. Comput. 12 (2024), no. 1, 1-52

12. Stochastic Heat Equation with general noise (with Yaozhong Hu), Ann. Inst. Henri Poincaré Probab. Stat. 58 (2022), no. 1, 379–423. 

Ph.D. thesis

• Some SPDEs/SDEs driven by fractional Gaussian noises and their related properties

     Faculty of Science Dissertation Award Winner at the University of Alberta

Teaching

Johns Hopkins University

• 2025 Spring: Instructor for AS. 110.653- Stochastic differential equations

  • 2025 Spring: Instructor for AS. 110.433- Applied harmonic analysis

  • 2024 Spring: Instructor for AS. 110.417- Partial differential equations

• 2024 Spring: Instructor for AS. 110.405- Real analysis I

• 2023 Spring: Instructor for AS. 110.202-Calculus III

• 2022 Fall: Instructor for AS. 110.108-Calculus I

University of Alberta

• 2022 Spring: Instructor for MATH 125- Linear Algebra

• 2022 Winter: Instructor for MATH 101- LABS- Calculus II

• 2021 Winter: Instructor for MATH 100- LABS- Calculus I

• 2018 Fall: Instructor for MATH-100- LABS- Calculus I

Scientific Agenda

2025

• • May 30, 2025. Speaker at the Departmental seminar, Department of Mathematics & Statistics, Concordia University

  • May 28, 2025. Speaker at the Statistical Society of Canada 2025 Annual Meeting, University of Saskatchewan

  • Apr 11, 2025. Speaker at the PDE/Applied Math seminar, Drexel University

2024

• • Nov 29- Dec 2, 2024. Speaker at CMS Winter Meeting-Optimization, control, dynamics and stochastic: interplay and applications, Kwantlen Polytechnic University 

  • Nov 6- 9, 2024. Visiting the Department of Mathematics and Statistics at Boston University

  • Nov 1-3, 2024. Speaker at SIAM New York-New Jersey-Pennsylvania Section Conference, Rochester Institute of Technology

  • Oct 11-14, 2024. Speaker at 7th Annual Meeting of SIAM Texas-Louisiana Section, Baylor University

  • Sep 6, 2024. Speaker at Probability Seminar of the Department of Mathematical and Statistical Sciences, University of Alberta

  • Aug 28, 2024. Speaker at the Seminar of Center for Mathematical Sciences and School of Mathematics and Physics, China University of Geosciences (Wuhan)

  • Aug 26-27, 2024. Speaker at the Seminar of Center for Mathematical Sciences and the Seminar of the School of Mathematics and Statistics, Huazhong University of Science and Technology

  • Aug 7, 2024. Speaker at Tianyuan Mathematical Center in Central China Seminar, Wuhan University

  • Aug 5-9, 2024. Summer school on Propagation of Chaos in Analysis and Probability, BICMR, Peking University  

  • Jul 30, 2024. Speaker at Mathematical Seminar Series, Great Bay University

  • Jul 15-16, 2024. Speaker at the NSF Computational Mathematics PI Meeting 2024, University of Washington at Seattle

  • Jun 23-28, 2024. Speaker at New Trends and Challenges in Stochastic Differential Games, BIRS workshop at the University of British Columbia Okanagan campus

  • May 20-22, 2024. Random Matrices and Applications, ICERM workshop at Brown University

  • May 6-10, 2024. Interacting Particle Systems: Analysis, Control, Learning and Computation, ICERM workshop at Brown University

  • Mar 26, 2024. Speaker at the Probability seminar, University of Tennessee

2023

• • Nov 10, 2023. Speaker at the Probability seminar, University of Rochester

  • Jun 28, 2023. Speaker at the seminar of the Department of Mathematics, Wuhan University of Science and Technology

  • Apr 12, 2023. Speaker at Stochastic Analysis Seminar at Auburn, Auburn University

  • Apr 4, 2023. Speaker at Johns Hopkins AMS Postdoc Seminar, Johns Hopkins University

• Mar 13, 2023. Speaker at Johns Hopkins Analysis & PDE Seminar, Johns Hopkins University

2022

• Aug 12 - Aug 13, 2022. Speaker at NSF/CBMS Follow-Up Conference: Gaussian Random Fields, Fractals, SPDEs, and Extremes, University of Alabama in Huntsville

• Jul 14, 2022. Speaker at Mathematics Seminars and Colloquia (in Mobile), Huazhong Agricultural University

• Jul 5, 2022. Speaker at Weekly Probability Seminar (in Mobile), Shandong University

2021

• Dec 3 - Dec 5, 2021. Speaker at Frontier Probability Days, University of Nevada in Las Vegas

• Nov 20 - Nov 21, 2021. Speaker at AMS special session on Stochastic Analysis and Applications (in Mobile), University of South Alabama

2019

• Jun 10 - Jun 14, 2019. Poster at Workshop on the Theory and Applications of Stochastic Partial Differential Equation, The Fields Institute

• Oct 19, 2019. Speaker at Graduate Colloquium, University of Alberta