CHAPTER 15
Stochastic Differential Equations
From ODEs to SDEs
Why random fluctuations are added to deterministic dynamics.
Drift and diffusion
Interpretation of the terms in dXₜ=a(Xₜ,t)dt+b(Xₜ,t)dWₜ.
Common SDE models
Brownian motion with drift, geometric Brownian motion and mean reversion.
Numerical simulation
Time discretisation and Euler–Maruyama.
SDEs in mathematical biology
Population and epidemic examples with stochastic trajectories.