Remains the issue of defining explicitly L . This can be done taking the expectation from the integral form of the Itô's lemma : E ( p ( X t ) ) = p ( X 0 ) + E ( ∫ ∫ 0 t ( ∂ ∂ t + μ μ ∂ ∂ x + σ σ 2 2 ∂ ∂ x 2 ) p ( X t ′ ) d t ′ ) .