On weak Brownian motions of arbitrary order 1
نویسندگان
چکیده
We show the existence, for any k 2 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 C0; 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 " > 0, there are weak Brownian motions whose law coincides with Wiener measure outside of any interval of length ". 1 Support of the EU through the TMR contract ERB-FMRX-CT96-0075 \Stochastic Analysis" and of Deutsche Forschungsgemeinschaft (Berliner Graduiertenkolleg "Stochastische Prozesse und probabilistische Analysis" and SFB 373 "Quantiication and Simulation of Economic Processes") is gratefully acknowledged. 2 On weak Brownian motions of arbitrary order
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