Mathematically, Wiener process is a continuous-time stochastic process named after norbert wiener. Because it is closely related to Brownian motion in physics, it is often called "Brownian motion process" or Brownian motion for short. Wiener process is one of the most famous Levi processes (which refers to the stationary independent incremental random process with left limit and right continuity), and it has important applications in pure mathematics, applied mathematics, economics and physics.

Wiener process is as important in pure mathematics as it is in applied mathematics. In pure mathematics, Wiener process leads to the study of continuous martingale theory, which is a basic tool to describe a series of important and complex processes. It is indispensable in the study of stochastic analysis, diffusion process and potential theory. In applied mathematics, Wiener process can describe the integral form of Gaussian white noise. In electronic engineering, Wiener process is an important part of establishing noise mathematical model. In cybernetics, Wiener process can be used to represent unknowable factors.

Wiener process is closely related to Brownian motion in physics. Brownian motion refers to the endless random motion of pollen particles suspended in liquid. Wiener motion can also describe other random motions determined by Fokker-Planck equation and Langevin equation. Wiener process forms the basis of strict path integral expression of quantum mechanics (according to Feynman-Katz formula, the solution of Schrodinger equation can be expressed by Wiener process). In financial mathematics, Wiener process can be used to describe options pricing models such as Black-Scholes model.