主题词：Stochastic processes and statistical mechanics; Stochastic processes and financial applications; Probability and Risk Models; Random Matrices and Applications; Mathematical Dynamics and Fractals; Financial Risk and Volatility Modeling; Markov Chains and Monte Carlo Methods; advanced mathematical theories; Bayesian Methods and Mixture Models; Advanced Mathematical Modeling in Engineering; Theoretical and Computational Physics; Point processes and geometric inequalities; Nonlinear Differential Equations Analysis; Mathematical Approximation and Integration; Advanced Algebra and Geometry; Complex Systems and Time Series Analysis; Advanced Combinatorial Mathematics; Advanced Harmonic Analysis Research; Stability and Controllability of Differential Equations; Statistical Methods and Inference; Advanced Banach Space Theory; Spectral Theory in Mathematical Physics; Diffusion and Search Dynamics; Geometric Analysis and Curvature Flows; Geometry and complex manifolds