We derive an adiabatic theory for a stochastic differential equation, εdX(s)=L1(s)X(s)ds+ε√L2(s)X(s)dBs, under a condition that instantaneous stationary states of L1(s) are also stationary states of L2(s). We use our results to derive the full statistics of tunneling for a driven stochastic Schr\”{o}dinger equation describing a dephasing process.
vitayard 