Before revision:  We also explicitly solve the case of a two stage diffusion model, and provide numerical demonstrations of the computations suggested by our analysis. Finally we present calculations that allow our techniques to approximate time-varying Ornstein-Uhlenbeck processes . By presenting these explicit formulae, we aim to foster the development of refined numerical methods and analytical techniques for studying diffusion decision processes with time-varying drift rates and thresholds .
After revision:  We also provide a review of how martingale theory may be used to analyze similar models employing Wiener processes by re-deriving some classical results. In concert with a variety of numerical tools already available, the current derivations should encourage mathematical analysis of more complex models of decision making with time-varying drift rates and thresholds .