Given a continuous stochastic process $x_t$ defined by the following Langevin equation
\begin{equation} d x_t = dB_t +F(x_t)dt \end{equation} where $dB_t$ is a Wiener increment and $F(x_t)$ is a general force such that $F(x_t)=-V'(x_t)/2$. It can be shown that this process, in the steady state, is sampled by the probability distribution
\begin{equation} P(x)=N e^{-V(x)} \end{equation} where $N$ is just a normalization. From this, all moments can be computed, i.e. $E[f(x)]=\int dx f(x) P(x)$.
I would like to compute now a two-time correlation function in the steady-state, i.e. $E[x(t) x(0)]$? Is it possible to do so from the probability function we found before? How should one proceed?