Generalization of h-Convex Stochastic Processes and Some Classical Inequalities

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....

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Bibliographic Details
Published in:Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-9
Main Authors: Li, Jingjng, Ghafoor, Mamoona, Saleem, Muhammad Shoaib, Zhou, Hao
Format: Article
Language:English
Subjects:
Axioms
Convex analysis
Expected utility
Inequalities
Inequality
Optimization
Probabilistic models
Probability theory
Random variables
Statistical analysis
Stochastic models
Stochastic processes
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Summary: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 h-convex stochastic processes is introduced, and some basic properties concerning generalized h-convex stochastic processes are developed. Furthermore, we establish Jensen and Hermite–Hadamard and Fejér-type inequalities for this generalization.
ISSN:1024-123X
1563-5147
DOI:10.1155/2020/1583807