The relationship between randomness and noise in stochastic differential equations

The concept of randomness in stochastic differential equations involves the rate of change of states and the presence of random noise in modeling systems. The debate lies in whether randomness exists intrinsically in the system or is a result of limitations in modeling accuracy. The presence of noise in the model can result in a stochastic differential equation with a stochastic term, making it different from an ordinary differential equation. The perspective on noise being Gaussian is common due to its representation of real-world phenomena, and the central limit theorem supports using Gaussian noise for accurate mathematical representations.