主题词：Probability and Risk Models; Stochastic processes and financial applications; Analytic Number Theory Research; advanced mathematical theories; Stochastic processes and statistical mechanics; Differential Equations and Boundary Problems; Mathematical Dynamics and Fractals; Advanced Mathematical Identities; Financial Risk and Volatility Modeling; Differential Equations and Numerical Methods; Advanced Mathematical Modeling in Engineering; Bayesian Methods and Mixture Models; Mathematical functions and polynomials; Mathematical Approximation and Integration; Meromorphic and Entire Functions; Functional Equations Stability Results; Advanced Algebra and Geometry; Advanced Harmonic Analysis Research; Statistical Methods and Inference; Advanced Banach Space Theory; Nonlinear Differential Equations Analysis; Random Matrices and Applications; Mathematics and Applications; Holomorphic and Operator Theory; Algebraic and Geometric Analysis