Research

Research Interests

• Probability theory and mathematical analysis

• Stochastic processes, random fields

• Stochastic partial differential equations

• Mathematical physics, statistics, mathematical finance, etc.

Publications and Preprints

1. Propagation of singularities for the damped stochastic Klein-Gordon equation. Submitted, 2025.
   (with Hongyi Chen) arxiv

2. On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation. Submitted, 2025
   (with Jingwu Hu) arxiv

3. On the passage times of self-similar Gaussian processes on curved boundaries. Submitted, 2025
   (with Davar Khoshnevisan) arxiv

4. Fourier dimension of the graph of fractional Brownian motion with H≥1/2. Submitted, 2025
   (with Chun-Kit Lai) arxiv

5. Hitting probabilities, thermal capacity, and Hausdorff dimension results for the Brownian sheet. Submitted, 2025
   (with Yimin Xiao) arxiv

6. Growth rate of liquidity provider's wealth in G3Ms. Submitted, 2024
   (with Shen-Ning Tung and Tai-Ho Wang) arxiv

7. Local times of anisotropic Gaussian random fields and stochastic heat equation. To appear in Ann. Inst. Henri Poincaré Probab. Stat.
   (with Yimin Xiao) arxiv

8. Tensor quantile regression with low-rank tensor train estimation. Ann. Appl. Stat. 18, no. 2, 1294–1318, 2024
   (with Zihuan Liu and Heping Zhang) journal

9. Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds. Stoch. Partial Differ. Equ. Anal. Comput. 12, 1507–1573, 2024
   (with David Candil and Le Chen) arxiv journal

10. Hitting probabilities of Gaussian random fields and collision of eigenvalues of random matrices. Trans. Amer. Math. Soc. 376, no. 6, 4273–4299, 2023
    (with Jian Song, Yimin Xiao and Wangjun Yuan) arxiv journal

11. Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields. Bernoulli 29, no. 1, 523–550, 2023
    (with Yimin Xiao) arxiv journal

12. Regularity of certain commutative Banach rings. J. Math. Anal. Appl. 517, no. 1, Paper No. 126589, 10 pp, 2023
    (with Chi-Wai Leung) journal

13. Local nondeterminism and local times of the stochastic wave equation driven by fractional-colored noise. J. Fourier Anal. Appl. 28, no. 2, Paper No. 26, 38 pp, 2022
    arxiv journal

14. The Hausdorff measure of the range and level sets of Gaussian random fields with sectorial local nondeterminism. Bernoulli 28, no.1, 277–306, 2022
    arxiv journal

15. Propagation of singularities for the stochastic wave equation. Stochastic Process. Appl. 143, 31–54, 2022
    (with Yimin Xiao) arxiv journal

16. Multiple points of Gaussian random fields. Electron. J. Probab. 26, no. 17, 25pp, 2021
    (with Robert C. Dalang, Carl Mueller and Yimin Xiao) arxiv journal

17. Local nondeterminism and the exact modulus of continuity for stochastic wave equation. Electron. Commun. Probab. 24 no. 52, 8pp, 2019
    (with Yimin Xiao) arxiv journal

18. Norm-attaining property for a dual pair of Banach spaces. J. Math. Anal. Appl. 445 no. 1, 556–563, 2017
    (with Chi-Wai Leung) journal