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A note on the sharp Lp-convergence rate of upcrossings to the Brownian local time

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  • Ohashi, Alberto
  • Simas, Alexandre B.

Abstract

In this note, we prove a sharp Lp-rate of convergence of the number of upcrossings to the local time of the Brownian motion. In particular, it provides novel p-variation estimates (2

Suggested Citation

  • Ohashi, Alberto & Simas, Alexandre B., 2015. "A note on the sharp Lp-convergence rate of upcrossings to the Brownian local time," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 137-141.
    • Handle: RePEc:eee:stapro:v:100:y:2015:i:c:p:137-141
    DOI: 10.1016/j.spl.2015.02.001
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    References listed on IDEAS

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    1. Knight, Frank B., 1997. "Approximation of stopped Brownian local time by diadic crossing chains," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 253-270, March.
    2. Blandine, Bérard Bergery & Pierre, Vallois, 2008. "Approximation via regularization of the local time of semimartingales and Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2058-2070, November.
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