Hermitian adjoint
Let "A"∗ denote the Hermitian adjoint of "A" (with respect to the "L"2 inner product). Then, given that the initial position "X"0 has a prescribed density ρ0, ρ("t", "x") is differentiable with respect to "t", ρ("t", ·) ∈ "DA"* for all "t", and ρ satisfies the following partial differential equation, known as the Fokker–Planck equation: