The Wiener process plays an important role in both pure and applied mathematics. In pure mathematics, the Wiener process gave rise to the study of continuous time martingales. It is a key process in terms of which more complicated stochastic processes can be described. As such, it plays a vital role in stochastic calculus, diffusion processes and even potential theory. It is the driving process of Schramm–Loewner evolution. In applied mathematics, the Wiener process is used to represent the integral of a white noise Gaussian process, and so is useful as a model of noise in electronics engineering (see Brownian noise), instrument errors in filtering theory and disturbances in control theory.
the wiener process plays an important role in both pure and applied mathematics in pure mathematics the wiener process gave rise to the study of continuous time martingales it is a key process in terms of which more complicated stochastic processes can be described as such it plays a vital role in stochastic calculus diffusion processes and even potential theory it is the driving process of schramm–loewner evolution in applied mathematics the wiener process is used to represent the integral of a white noise gaussian process and so is useful as a model of noise in electronics engineering (see brownian noise) instrument errors in filtering theory and disturbances in control theory