  We present a class of scalar Markovian diffusion processes whose transition
probability densities are skewed Gaussian distributions. Their stochastic
dynamics involve nonlinear and time-dependent drifts driven by White Gaussian
noise sources. The drifts are obtained via generalized $h$-transforms of a
novel class of local martingales. We can alternatively represent this class of
processes as dynamic censoring models with partial observability and
time-dependent correlations, which can be used as a skewness-inducing noise
source for any diffusion process. We prove the invariance of our class of
skew-Normal processes under linear transformations. We extend our results to
Ornstein-Uhlenbeck diffusions.
