Stochastic Differential Equation

A differential equation in which one or more terms are stochastic processes, typically written with a drift term and a diffusion term driven by a continuous martingale such as Brownian motion, and interpreted in a stochastic calculus sense (Itô or Stratonovich).

A differential equation in which one or more terms are stochastic processes (random signals), so solutions are random processes; typically written using differential notation that encodes stochastic integrals (e.g., driven by Brownian motion or Lévy noise).