Stochastic Differential Equations

Extend deterministic differential equations to models with continuous random variation. Develop Brownian motion, drift and diffusion, Itô processes, numerical simulation, moments and the relationship between deterministic, CTMC and SDE descriptions.

01Brownian motion 02Brownian increments 03Drift and diffusion 04Itô processes 05Itô's lemma 06SDE biological models 07Euler–Maruyama method 08Mean and variance 09Moment equations 10Moment closure 11Deterministic versus CTMC versus SDE models