Some properties of <em>η</em>-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 η-convex stochastic process is introduced in this paper. Moreover some basic properties of η-convex stochastic process are derived. We also derived Jensen, Hermite–Hadamard and Ostrowski type inequalities for η-convex stochastic process.

Keywords

• stochastic process
• <i>η</i>-convex function
• <i>η</i>-convex stochastic processes
• hermite hadmard type inequality
• ostrowski type inequality and jensen inequality