Seminário de Sistemas Dinâmicos e Estocásticos - Path integral formalism and time reversibility for multiplicative white noise stochastic differential equations (SDE).

We present a functional formalism to derive a generating functional for correlation functions of a
multiplicative stochastic process represented by a Langevin equation in a general stochastic prescription
. A path integral over a set of non-commutative variables without performing any time discretization
will be deduced. In multiplicative white noise SDE, trajectories evolve with di erent prescriptions in one
direction and in the reverse direction. We will carefully de ne the time reversal transformation for this
kind of processes, taking into account that the asymptotic stationary probability distribution depends on
the stochastic integral prescription.