ABSTRACT
Diffusion models appear throughout applied mathematics, and form a natural stochastic generalization of differential equations (DEs). In a first-order DE such as dy = f (y, t) dt, the idea is that as time advances a small amount h, the value of y changes by the small amount f (y, t) · h. This naturally gives rise to a numerical method: keep updating time by adding h to the current time value at each step, while updating y by adding f (y, t) · h to the current y value at each step. For many DE’s, only such numerical solutions are possible.
