P-Superquadratic Stochastic Processes via Fractional Stochastic Calculus with Applications to Divergence Measures

The notion of P-superquadratic stochastic processes, a new extension and improvement of conventional superquadratic stochastic processes, is presented and thoroughly developed in this work. In the context of mean-square stochastic calculus, we methodically examine their fundamental structural characteristics and use them to develop sophisticated versions of Jensen's inequality and (Hermite-Hadamard) H.H-type inequalities. The stochastic (Riemann-Liouville) RL fractional integrals are used to further extend these inequalities to their fractional counterparts, offering a more comprehensive analytical toolset for fractional stochastic analysis. Theoretical conclusions are supported by thorough tabular representations and graphical visualisations that are built from a variety of instructive cases. We also formulate new classes of stochastic divergence measures to show that the proposed framework is applicable in information theory. We give direct access to the commands used to create all graphs and tables, as well as the times at which each computation was executed, enabling repeatability and computational transparency.

کلیدواژه ها:

Mean-square stochastic RL fractional integrals ، P-superquadratic stochastic process ، Jensen's inequality ، H.H's inequality ، Stochastic divergence ، RL fractional stochastic H.H-divergence