On 10/01/2026, at the Nguyen Van Cu Campus, VNUHCM-University of Science (HCMUS) held the institutional-level doctoral thesis defence for researcher Thái Phúc Hưng (cohort 2022–2025), specialising in Probability Theory and Mathematical Statistics, under the academic supervision of Prof. Đặng Đức Trọng. The thesis, entitled “Non-parametric estimation for some stochastic processes”, focuses on solving non-parametric estimation problems within the framework of stationary α-mixing processes—a crucial class of models in modern statistics, particularly when data exhibits time dependence and is subject to noise.

Regarding the content, the thesis is developed along two main research directions. Firstly, the research employs methods to estimate the invariant probability density function of stationary α-mixing processes based on noisy observations, where noise is modelled as a stationary α-mixing process with a known invariant density function. Results were established for both ordinary smooth and supersmooth noise, thereby extending results previously published in international journals.

Secondly, the thesis examines the problem of estimating the probability Ρ (X < Y) in the context of two stationary α-mixing processes with paired observations affected by noise. This approach extends the stress–strength problem from the assumption of independent random variables to time-dependent models, which are more suitable for various types of real-world data.

One of the prominent theoretical contributions of the thesis is the establishment of the lower bound for the mean square error of the estimator in noisy data models for α-mixing processes, thus proving minimax optimality with an optimal convergence rate. Furthermore, assumptions regarding noise are significantly relaxed by allowing noise to be a stationary α-mixing process instead of the standard assumption of independent and identically distributed random variables.

Beyond its theoretical significance, the findings demonstrate clear practical applications, particularly in finance, medicine, and data science. In the thesis, the proposed method was applied to analyse real data on creatine kinase enzyme levels in healthy individuals and patients with Duchenne Muscular Dystrophy (DMD), as well as in stress–strength model analysis and ROC curve evaluation to support medical diagnostic efficiency.

In addition to the achieved results, the thesis suggests several further research directions concerning estimation in models with multiplicative noise, unknown noise, and complex models, showing the long-term development potential of this research field.

The Examination Committee attended and raised questions for researcher Thái Phúc Hưng. The defence session was highly commended by the Committee for its novelty, mathematical rigour, and potential for further development. The Committee reached a consensus to recommend the conferment of the degree of Doctor of Mathematics upon researcher Thái Phúc Hưng.