Wiener process

A Wiener process, also known as Brownian motion, is a mathematical model used to describe random, continuous fluctuations over time—like the unpredictable movement of a particle suspended in fluid. It features three key properties: the changes are continuous, the steps are independent, and the movement has no preferred direction, making it steady over time. This concept is widely used in finance, physics, and engineering to model unpredictable systems, such as stock prices or particle diffusion, capturing the inherent randomness and unpredictability in these processes.