  In this paper we propose a new type of viscosity solutions for fully
nonlinear path dependent PDEs. By restricting to certain pseudo Markovian
structure, we remove the uniform non- degeneracy condition imposed in our
earlier works [9, 10]. We establish the comparison principle under natural and
mild conditions. Moreover, as applications we apply our results to two
important classes of PPDEs: the stochastic HJB equations and the path dependent
Isaacs equations, induced from the stochastic optimization with random
coefficients and the path dependent zero sum game problem, respectively.
