Euler–Maruyama: SDEs as Limits of Algorithms

Stochastic differential equations cannot usually be solved with paper and pencil. We must discretize them in time, and the simplest approach is the Euler-Maruyama scheme.

At each step, we advance along the drift by delta t, and along the diffusion by root delta t times standard normal noise. Notice the square root: diffusion scales with the square root of time.

The rest of the narration is in the book's Companion.