Can anyone provide an example (as simple as they like) of a process $X_t$ on $\mathbb{R}$ solution to $dX=\sigma (X,t)dt+b(X,t)dW$. Where $W$ is a Brownian Motion, and $\sigma$ and $b$ can be any coefficients. And there exists a reversible distribution $\pi$ for $X$ defined in the usual way through the semi-group.
Any example will do, I don't know one.
Edit :
The answerer is free to choose the SDE, the probability space, and the distribution $\pi$. But please can the solution to the SDE $X_t$ take values in $\mathbb{R}$.
Please no degenerate answers, like a process which is deterministic.