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Föllmer, Hans
Wu, Ching-Tang
Yor, Marc
Year of Publication: 
Series/Report no.: 
Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1999,89
We show the existence, for any k E N, of processes which have the same k-marginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law P' of such a weak Brownian motion of order k can be constructed to be equivalent to Wiener measure P' on c [O, 1]. On the other hand, there are weak Brownian motions of arbitrary order whose law is singular to Wiener measure. We also show that, for any e > 0, there are weak Brownian motions whose law coincides with wiener measure outside of any interval of length e.
Brownian motion
weak Brownian motion
weak martingale
Volterra kernel
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Working Paper

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