On weak Brownian motions of arbitrary order

Arbeitspapier

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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: SFB 373 Discussion Paper ; No. 1999,89

Klassifikation und Themen

• Klassifikation: Wirtschaft
• Thema: Brownian motion ; weak Brownian motion ; weak martingale ; marginals ; Volterra kernel

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Föllmer, Hans ; Wu, Ching-Tang ; Yor, Marc
• Ereignis: Veröffentlichung
• (wer): Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes
• (wo): Berlin
• (wann): 1999

Weitere Informationen

• Handle: http://hdl.handle.net/10419/61756
• URN: urn:nbn:de:kobv:11-10046769
• Letzte Aktualisierung: 10.03.2025, 11:43 MEZ