In the introduction of a paper I was reading the author writes without elaborating that
" In the case of a non-degenerate diffusion coefficient, Stroock and Varadhan , proved the existence of a unique weak solution for a SDE with bounded measurable drift , and bounded continuous diffusion coefficients. "
So if the SDE is $$ dX_t=\mu(X_t)dt+\sigma(X_t)dB_t $$
So what does non-degeneracy of the diffusion coefficient mean here? Does it mean that $\sigma(X_t)\sigma(X_t)^T$ is invertible for all $t\ge 0$ almost surely? Or does it say something directly about the function $\sigma$?