Imagen de Portada

Fractional Mean-Square Inequalities for (P, m)-Superquadratic Stochastic Processes and Their Applications to Stochastic Divergence Measures

Guardado en:
Publicado en:Fractal and Fractional vol. 9, no. 12 (2025), p. 771-804
Autor principal: Khan, Dawood
Otros Autores: Butt, Saad Ihsan, Jallani Ghulam, Alammar Mohammed, Seol Youngsoo
Publicado:
MDPI AG
Materias:
Cryptography
Control theory
Calculus
Divergence
Stochastic processes
Inequalities
Mathematical analysis
Computer science
Random variables
Mathematical models
Integrals
Design
Convex analysis
Stochastic models
Engineering
Mathematics
Fractional calculus
Information theory
Differential equations
Data compression
Acceso en línea:Citation/Abstract
Full Text + Graphics
Full Text - PDF
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
Resumen:In this study, we introduce and rigorously formalize the notion of (P, m)-superquadratic stochastic processes, representing a novel and far-reaching generalization of classical convex stochastic processes. By exploring their intrinsic structural characteristics, we establish advanced Jensen and Hermite–Hadamard (<inline-formula>H.H</inline-formula>)-type inequalities within the mean-square stochastic calculus framework. Furthermore, we extend these inequalities to their fractional counterparts via stochastic Riemann–Liouville (<inline-formula>RL</inline-formula>) fractional integrals, thereby enriching the analytical machinery available for fractional stochastic analysis. The theoretical findings are comprehensively validated through graphical visualizations and detailed tabular illustrations, constructed from diverse numerical examples to highlight the behavior and accuracy of the proposed results. Beyond their theoretical depth, the developed framework is applied to information theory, where we introduce new classes of stochastic divergence measures. The proposed results significantly refine the approximation of stochastic and fractional stochastic differential equations governed by convex stochastic processes, thereby enhancing the precision, stability, and applicability of existing stochastic models. To ensure reproducibility and computational transparency, all graph-generation commands, numerical procedures, and execution times are provided, offering a complete and verifiable reference for future research in stochastic and fractional inequality theory.
ISSN:2504-3110
DOI:10.3390/fractalfract9120771
Fuente:Engineering Database