On weak Brownian motions of arbitrary order
A weak Brownian motion of order \(k\) is a stochastic process having the same \(k\)-dimensional marginals as Brownian motion. The authors prove the existence of continuous weak Brownian motions of any order; this is done with the corresponding law on Wiener space both equivalent or singular to Wiener measure. Moreover, they show that there are even weak Brownian motions whose law coincides with Wiener measure outside of any interval of length \(\varepsilon\).
scientific article; zbMATH DE number 1525674