  We study the asymptotic behaviour of a properly normalized time changed
Wiener processes. The time change reflects the fact that we consider the
Laplace operator (which generates a Wiener process) multiplied by a possibly
degenerate state-space dependent intensity $\lambda(x)$. Applying a functional
limit theorem for the superposition of stochastic processes, we prove
functional limit theorems for the normalized time changed Wiener process. The
normalization depends on the asymptotic behaviour of the intensity function
$\lambda$. One of the possible limits is a skew Brownian motion.
