Articles
1. Existence, uniqueness and ergodic properties for time-homogeneous Itô-SDEs with locally integrable drifts and Sobolev diffusion coefficients
(with G. Trutnau) (Tohoku Mathematical Journal 73 (2021), 159–198) (Journal link) (Arxiv link)
2. Existence and regularity of infinitesimally invariant measures, transition functions and time homogeneous Itô-SDEs
(with G. Trutnau) (Journal of Evolution Equations, 601-623(2021) (Journal link) (Arxiv link)
3. Well-posedness for a class of degenerate Itô-Stochastic Differential Equations with fully discontinuous coefficients
(with G. Trutnau) (Symmetry 2020, 12(4), 570) Special Issue 'Advances in Stochastic Differential Equations'
(Journal link) For the detailed version, (Arxiv link)
4. Existence and uniqueness of (infinitesimally) invariant measures for second order partial differential operators on Euclidean space
(with G. Trutnau) (Journal of Mathematical Analysis and Applications, Volume 507, Issue 1, 1 March 2022, 125778)
5. (Book) Analytic theory of Itô-stochastic differential equations with non-smooth coefficients (with G. Trutnau, W. Stannat)
SpringerBriefs in Probability and Mathematical Statistics 2022 (SBPMS) (Journal Link), (Arxiv link)
6. Conservativeness and uniqueness of invariant measures related to non-symmetric divergence type operators
(Stochastics 95 (2023), no.4, 635-661) (Journal link) (Arxiv link)
7. On the pathwise uniqueness for a class of degenerate Itô-stochastic differential equations
(Osaka Journal of Mathematics, 60 (2023), 533–543) (Journal link) (Arxiv link)
8. Strong uniqueness of finite dimensional Dirichlet operators with singular drifts
(Infinite Dimensional Analysis, Quantum Probability and Related Topics, 26(2023), no.03, Paper No. 2350009)
9. On the contraction properties for weak solutions to linear elliptic equations with L2-drifts of negative divergence
(Proceedings of the American Mathematical Society, 152(5), May 2024, page 2051–2068) (Journal link) (Arxiv link)
10. Error estimates of Physics-Informed Neural Networks for initial value problems (with J. Yoo, J. Kim, M. Gim)
(Journal of the Korean Society for Industrial and Applied Mathematics, Vol. 28, No. 1, March, 2024, page 33-58) (Journal link)
11. Uniqueness in law for singular degenerate SDEs with respect to a (sub-)invariant measure
(with G. Trutnau) (Arxiv link)
12. Pointwise well-posedness results for degenerate Itô-SDEs with locally bounded drifts
(with G. Trutnau) (Arxiv link)
13. Uniform approximation by harmonic polynomials for solving the Dirichlet problem of Laplace's equation on a disk
14. Robust error estimates of PINN in one-dimensional boundary value problems for linear elliptic equations
(with J. Yoo) (Arxiv link)
Ph.D. Thesis
Analytic Approach to Invariant Measures and Itô-Stochastic Differential Equations
(Seoul National University, 2019.8) (S-space link)