Chapter 4 describes three mathematical methods used to obtain response time distribution and accuracy predictions for diffusion process models, including models in which the drift and diffusion rates vary over time or as a function of evidence state. The latter include Ornstein–Uhlenbeck models, urgency models, and models with collapsing-decision boundaries. The first, classical, infinite series representation, for the constant drift and constant diffusion Wiener process, is obtained by inverting the moment generating function derived from the Wald identity. The second method is is the integral equation method, which arises from a general renewal representation of a diffusion process, with possibly time-dependent and state-dependent drift and diffusion rates between possibly time-dependent decision boundaries. The third method is the matrix method, which approximates a diffusion process with a finite-state Markov chain, The method is closely related to the Crank–Nicolson method for solving the Kolmogorov backward and forward equations numerically. The chapter discusses applications in which a researcher may prefer one method over another.