I have got a multivariate nonlinear SDE: $$ dX(t) = f(X(t))\,dt+\Sigma\, dW(t),\, t\in(-\infty,\infty), $$ where $X(t)\in\mathbb{R}^d$, $f:\mathbb{R}^d\to \mathbb{R}^d$ is a "Lipschitz" continuous function (in the Euclidean norm), $\Sigma\in\mathbb{R}^{d\times d}$ is a symmetric and positive definite matrix, and $W(t)\in\mathbb{R}^d$ is a standard multivariate Wiener process.
My question is: are there conditions on $f$ and $\Sigma$ such that $X(t)$ is strictly stationary? By the strictly stationarity, I mean for any $n\in\mathbb{N}$ and $t_1,...,t_n\in\mathbb{R}$,
$$
(X(t_1),...,X(t_n))\stackrel{d}{=}(X(t_1+\tau),...,X(t_n+\tau))
$$
for any $\tau\in\mathbb{R}$.
I understand that it is possible to obtain an analytic solution to $X(t)$ (using the formula on p.60 of the slides here: https://www.ethz.ch/content/dam/ethz/special-interest/mavt/dynamic-systems-n-control/idsc-dam/Lectures/Stochastic-Systems/SDE.pdf). However, this does not help me much, because I would like to leave $f$ unspecified for the moment. Another fact is that if $f$ is linear, then the SDE becomes linear and clearly one can find a stationary analytic solution for $X(t)$.
Thank you!