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Rates of convergence to Brownian local time

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  • Bass, Richard F.
  • Khoshnevisan, Davar

Abstract

Suppose Sn is a mean zero, variance one random walk. Under suitable assumptions on the increments, we prove a strong approximation theorem for the local times of Sn to the local times of a Brownian motion, uniformly at all levels.

Suggested Citation

  • Bass, Richard F. & Khoshnevisan, Davar, 1993. "Rates of convergence to Brownian local time," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 197-213, September.
  • Handle: RePEc:eee:spapps:v:47:y:1993:i:2:p:197-213
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    Cited by:

    1. Antoine Lejay, 2018. "Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 539-551, October.
    2. Csáki, Endre & Csörgo, Miklós & Földes, Antónia & Révész, Pál, 2011. "On the local time of random walk on the 2-dimensional comb," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1290-1314, June.

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