Spontaneous emission of an atom in contact with the modified radiation field of a Photonic band gap (PBG) material is known to present a typically non-Markovian behavior. In addition, the presence of a gap of forbidden frequencies in the photonic density of states (DOS), produces residual population of the excited level, and population inversion when the atomic system is driven by an external laser field. It's our aim to study those effects using non-Markovian Stochastic Schroedinger equations (NMSSE). This formalism permit us to describe the evolution of the atom in terms of a wave function, |ψt(z)], which due to the presence of the radiation field depends on a stochastic variable zt. Having a singularity at the origin, the models of field correlation function usually found in literature, are not suitable to generate the corresponding zt. We have proposed a new correlation function that do not have this problem, and reproduces all the important physical phenomena of the system under study. The results obtained with NMSSE are compared
with those of the master equation, since the ensemble average of stochastic trajectories gives the reduced density matrix of the system, ρs. In addition, we propose a new non-Markovian master equation derived from the stochastic formalism, which in contrast to the current models of master equation preserves positivity for the problem under study.