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On weak Brownian motions of arbitrary order

Author

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  • Föllmer, Hans
  • Wu, Ching-Tang
  • Yor, Marc

Abstract

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.

Suggested Citation

  • Föllmer, Hans & Wu, Ching-Tang & Yor, Marc, 1999. "On weak Brownian motions of arbitrary order," SFB 373 Discussion Papers 1999,89, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199989
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