pr=ItoProcess[ItoProcess[{0,1,{w[t],w[t]^4-6 w[t]^2 t+3 t^2}},w,t]]

residuals[mthd_]:=Block[{td},td=RandomFunction[pr,{0.,1,.01},1250,Method->mthd];
Histogram[Function[{x,y},y-(x^4-6 x^2+3)]@@@Part[td["States"],All,-1],ImageSize->250,PlotRange->{{-1,1},Automatic},PlotRangeClipping->True,PlotLabel->mthd,Frame->True,Axes->False]]

{{residuals["EulerMaruyama"],residuals[Automatic]},
{residuals["Milstein"],residuals["StochasticRungeKutta"]},
{residuals["KloedenPlatenSchurz"],residuals["StochasticRungeKuttaScalarNoise"]}}//Grid