In today’s post, we will explore numerical schemes for integrating stochastic differential equations in Mathematica. We will take an informal approach; for an in-depth treatment of stochastic differential equations, I recommend that you look at Stochastic Processes for Physicists by Kurt Jacobs and Modeling with Ito Stochastic Differential Equations by Edward Allen.

Ecologists commonly collect data representing counts of organisms. Generalized linear models (GLMs) provide a powerful tool for analyzing count data.1 The starting point for count data is a GLM with Poisson-distributed errors, but not all count data meet the assumptions of the Poisson distribution.

Mathematica’s NDSolve command is great for numerically solving ordinary differential equations, differential algebraic equations, and many partial differential equations. Most of the integration details are handled automatically, out of the user’s sight.