Algebraic formulation of the SDE-path integral correspondence

Abstract: Any stochastic ordinary differential equation admits an equivalent path integral description. Borrowing techniques from the algebraic approach to quantum field theory, we propose an alternative formulation of this correspondence, focused on the computation of expectation values and correlation functions of the perturbative solution. In addition this approach highlights an interesting interplay with the Ito and Stratonovich definition of stochastic integral. Eventually the SDE framework serves as a starting point to fully grasp a possible extension to a perturbative path integral formulation of stochastic PDEs.