We analyze the statistical averages over a set of realizations of the random variable in the Stochastic Optical Bloch equations, using Novikov's sufficient condition theorem. We consider a system on an adiabatic basis interacting with an external field in the presence of a thermal reservoir. We analyzed both for delta-correlated functions (white noise) and situations associated with Ornstein-Uhlenbeck processes (OUP) in colored noise. The effects of thermal reservoir and intramolecular coupling generate an effective transversal relaxation time. In the case of white noise, the resulting optical Bloch equations can be solved algebraically, unlike colored noise cases that requires numerical techniques.