SDE biological models

SDEs extend differential-equation models by including continuous random fluctuations.

A stochastic population model may be written

The function \(f\) represents the deterministic biological mechanism, while \(g\) specifies how noise magnitude depends on the state.

Choosing the noise

The diffusion term should have a biological or mathematical justification. In diffusion approximations of event-based models, it can be derived from underlying transition rates rather than added arbitrarily.