Generalization of - Convex Stochastic Processes and Some Classical Inequalities

Hao Zhou, Muhammad Shoaib Saleem, Mamoona Ghafoor and Jingjng Li

Mathematical Problems in Engineering, 2020, vol. 2020, 1-9

Abstract:

The field of stochastic processes is essentially a branch of probability theory, treating probabilistic models that evolve in time. It is best viewed as a branch of mathematics, starting with the axioms of probability and containing a rich and fascinating set of results following from those axioms. In probability theory, a convex function applied to the expected value of a random variable is always bounded above by the expected value of the convex function of the random variable. In this paper, the concept of generalized - convex stochastic processes is introduced, and some basic properties concerning generalized - convex stochastic processes are developed. Furthermore, we establish Jensen and Hermite–Hadamard and Fejér-type inequalities for this generalization.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:1583807

DOI: 10.1155/2020/1583807

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