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 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.
Highlights
Stochastic processes are a branch of probability theory, treating probabilistic models that evolve in time [1,2,3]
It is a branch of mathematics, starting with the axioms of probability and containing a rich and fascinating set of results following from those axioms [4]
Stochastic processes have many applications in statistics, which obviously lead to lots of other domains, for example, Kolmogorov–Smirnoff test on the equality of distributions [38,39,40]. e other applications include sequential analysis [41, 42]
Summary
Stochastic processes are a branch of probability theory, treating probabilistic models that evolve in time [1,2,3]. Nikodem in 1980 introduced the convex stochastic processes in his article [17] Following this line of investigation, Skowronski described the properties of Jensen-convex and Wright-convex stochastic processes in [18, 19]. 2. Novelty and Significance e study of convex functions makes them special because of their interesting properties as maximum are attained at the boundary point, and any local minimum is global one. Novelty and Significance e study of convex functions makes them special because of their interesting properties as maximum are attained at the boundary point, and any local minimum is global one This topic of research got the attention of many researchers of different areas because of their enormous applications in optimization theory. For more details related to this work, see [25,26,27,28,29,30,31]
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