Approximating the Density of Random Differential Equations with Weak Nonlinearities via Perturbation Techniques

We combine the stochastic perturbation method with maximum entropy principle to construct approximations of first probability density function steady-state solution a class nonlinear oscillators subject small perturbations in term and driven by excitation. The nonlinearity depends both upon position velocity, excitation is given stationary Gaussian process certain additional properties. Furthermore, we approximate higher-order moments, variance, correlation functions solution. theoretical findings are illustrated via some numerical experiments that confirm our reliable.