Solution
= Solution
Define the <Multivariate Fokker-Planck probability current> by
$$
\boxed{J_i=A_iP-\frac12\frac{\partial}{\partial x_j}(B_{ij}P).}
$$
Then
$$
-\frac{\partial J_i}{\partial x_i}
=-\frac{\partial}{\partial x_i}(A_iP)
+\frac12\frac{\partial^2}{\partial x_i\partial x_j}(B_{ij}P),
$$
so the <Fokker-Planck equation> is exactly the <continuity equation> $\partial_tP+\nabla\cdot\mathbf J=0$.