Random differential inequalities and comparison principles for nonlinear hybrid random differential equations

In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities have been proved for an IVP of first order hybrid random differential equations with the linear perturbation of second type. A comparison theorem is proved and applied to prove the uniqueness of random solution for the considered perturbed random differential equation. Finally an existence of extremal random solution is obtained in between the given upper and lower random solutions.