Motion of a Hamiltonian nonlinear oscillator driven by a weak stochastic external force with broad spectrum is considered.At long times behavior of trajectories in phase space can be described statistically using the diffusion approximation.The latter applies when phase correlations between close trajectories rapidly decay,that prevents from existence of domains of stability and guarantees ergodic mixing.Domains of stability correspond to those trajectories,which are insensitive to small variations of initial conditions.So the following question arises:how rapidly phase correlations decay? For the sake to estimate how long domains of stability exist we construct the map,which makes them apparent,if they survive till the any time horizon τ0.