Wiener Space

Wiener space is the space of continuous paths which start at the origin, equipped with the Wiener measure. Under this probability measure, the coordinate maps form a -dimensional Wiener process. A typical path is continuous but nowhere differentiable and has nonzero quadratic variation.

Wiener space is the basic path-space model for Brownian motion and provides the setting for stochastic integration and the Malliavin calculus.