In mathematics, a brownian sheet is a multiparametric generalization of the brownian motion to a gaussian random field. This means we generalize the "time" parameter of a brownian motion from to . The exact dimension of the space of the new time parameter varies from authors. We follow John B. Walsh and define the -brownian sheet, while some authors define the brownian sheet specifically only for , what we call the -brownian sheet. (n,d)-Brownian sheet A -dimensional gaussian process is called a -brownian sheet if it has zero mean, i.e. for all for the covariance function for . Properties From the definition follows almost surely. Examples -brownian sheet is the brownian motion in . -brownian sheet is the brownian motion in . -brownian sheet is a one-dimensional brownian motion on the index set . Literature References Wiener process Robert Brown (botanist, born 1773)