Approximation of Time-changed Brownian motion

Time change is one of the most basic and useful transformations for Markov processes. In this talk, we present a general approximation scheme to the time-changed Brownian motion by the positive continuous additive functional associated with any Radon measure that does not charge zero capacity sets and has full quasi support. With some mild conditions on the Radon measure, point-wise starting approximation can be established. The convergence is shown in the Skorokhod topology. This talk is based on a joint work with Zhen-Qing Chen.