Some properties of η-convex stochastic processes

Abstract

The stochastic processes is a significant branch of probability theory, treating probabilistic models that develop in time. It is a part of mathematics, beginning with the axioms of probability and containing a rich and captivating arrangement of results following from those axioms. In probability, a convex function applied to the expected value of an random variable is always bounded above by the expected value of the convex function of the random variable. The definition of eta-convex stochastic process is introduced in this paper. Moreover some basic properties of eta-convex stochastic process are derived. We also derived Jensen, Hermite-Hadamard and Ostrowski type inequalities for eta-convex stochastic process.