The equation can be recast into a linear operator form, using the idea of infinitesimal generator. Define the linear operator A f := ∑ ∑ n = 1 ∞ ∞ ( − − ∂ ∂ x ) n [ D n ( x , t ) f ( x , t ) ] then the equation above states ∂ ∂ t p ( x , t ) = A p ( x , t ) ∂ ∂ t p ( x , t | x 0 , t 0 ) = A p ( x , t | x 0 , t 0 ) In this form, the equations are precisely in the form of a general Kolmogorov forward equation. The backward equation then states that ∂ ∂ t p ( x 1 , t 1 | x , t ) = − − A † † p ( x 1 , t 1 | x , t ) where A † † f := ∑ ∑ n = 1 ∞ ∞ D n ( x , t ) ∂ ∂ x n [ f ( x , t ) ] is the Hermitian adjoint of A .