Armed at the difficult solution of uncontrolled random nonlinear systems

a method for any order approximate solution of the state equation for uncontrolled random nonlinear systems is proposed. Based on general Langevin gradient equation in uncontrolled state space

the random nonlinear Volterra’s integral equation for the second kind

which is equivalent to general Langevin gradient equation

is obtained

by utilizing constant variation method.Then

any order approximate solution of the equation is also obtained

by successive approximation method.Finally

the influences of nonlinearity and randomness for state space transformation of the system is discussed.The method for any order approximate solution of the state equation for uncontrolled random nonlinear systems is an effective method of quantitative analysis for random nonlinear systems.