Asymptotic behaviour and functional limit theorems for a time changed Wiener process

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