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On almost sure convergence of the quadratic variation of Brownian motion

Author

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  • Levental, Shlomo
  • Erickson, R. V.

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.

Suggested Citation

  • Levental, Shlomo & Erickson, R. V., 2003. "On almost sure convergence of the quadratic variation of Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 106(2), pages 317-333, August.
    • Handle: RePEc:eee:spapps:v:106:y:2003:i:2:p:317-333
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