Functional integral approach for multiplicative stochastic processes

Understand

We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation.

• We deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization.
• The usual prescriptions to define the Wiener integral appear in our formalism in the definition of Green functions in the Grassman sector of the theory.
• We also study non-perturbative constraints imposed by BRS symmetry and supersymmetry on correlation functions.