Chen, Zhen-QingYu, Yang2024-10-162024-10-162024Yu_washington_0250E_27438.pdfhttps://hdl.handle.net/1773/52564Thesis (Ph.D.)--University of Washington, 2024We give a general discrete approximation scheme of time-changed Brownian motions on $\mathbb{R}^d$. Our approximation scheme works for any smooth measure with full quasi-support on $\mathbb{R}^d$ with suitable initial distributions. Under some mild conditions on the smooth measure, the discrete approximation scheme works for every starting point.application/pdfen-USCC BY-NC-NDMathematicsMathematicsThesis