Positive solutions to a class of random operator equations and applications to stochastic integral equations

We study the existence of random positive solutions to a random operator equation on ordered Polish spaces. We apply the results obtained in this paper to study the existence of random positive solutions to some classes of stochastic integral equations

Random Fixed Point Theorems of Random Comparable Operators and an Application

We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. Finally, as an application, we consider the existence of the solution of a random Hammerstein integral equation