On almost sure convergence of the quadratic variation of Brownian motion

We study the problem of a.s. convergence of the quadratic variation of Brownian motion. We present some new sufficient and necessary conditions for the convergence. As a byproduct we get a new proof of the convergence in the case of refined partitions, a result that is due to Lévy. Our method is based on conversion of the problem to that of a Gaussian sequence via decoupling.

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Year of publication:	2003
Authors:	Levental, Shlomo ; Erickson, R. V.
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 106.2003, 2, p. 317-333
Publisher:	Elsevier
Keywords:	Brownian motion Quadratic variation A.s. convergence

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008874339