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On weak Brownian motions of arbitrary order. (English) Zbl 0968.60069
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 \(\varepsilon\).

MSC:
60J65 Brownian motion
45D05 Volterra integral equations
60G15 Gaussian processes
60G48 Generalizations of martingales
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