On almost sure convergence of the quadratic variation of Brownian motion

Shlomo Levental and R. V. Erickson

Stochastic Processes and their Applications, 2003, vol. 106, issue 2, 317-333

Abstract: 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.

Keywords: Brownian; motion; Quadratic; variation; A.s.; convergence (search for similar items in EconPapers)
Date: 2003
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