  We present a study of the vacuum transition probabilities taking into account
quantum corrections. We first introduce a general method that expand previous
works employing the Lorentzian formalism of the Wheeler-De Witt equation by
considering higher order terms in the semiclassical expansion. The method
presented is applicable in principle to any model in the superspace and up to
any desired order in the quantum correction terms. Then, we apply this method
to obtain analytical solutions for the probabilities up to second quantum
corrections for homogeneous isotropic and anisotropic universes. We use the
Friedmann-Lemaitre-Robertson-Walker with positive and zero curvature for the
isotropic case and the Bianchi III and Kantwowski-Sachs metrics for the
anisotropic case. Interpreting the results as distribution probabilities of
creating universes by vacuum decay with a given size, we found that the general
behaviour is that considering up to the second quantum correction leads to an
avoidance of the initial singularity. However, we show that this result can
only be achieved for the isotropic universe. Furthermore, we also study the
effect of anisotropy on the transition probabilities.
