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Approximation via regularization of the local time of semimartingales and Brownian motion

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  • Blandine, Bérard Bergery
  • Pierre, Vallois

Abstract

Through a regularization procedure, a few schemes for approximation of the local time of a large class of continuous semimartingales and reversible diffusions are given. The convergence holds in the ucp sense. In the case of standard Brownian motion, we have been able to bound the rate of convergence in L2, and to establish the a.s. convergence of some of our schemes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:11:p:2058-2070
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    References listed on IDEAS

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    1. Russo, Francesco & Vallois, Pierre, 1995. "The generalized covariation process and Ito formula," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 81-104, September.
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    Cited by:

    1. Almada Monter, Sergio Angel, 2015. "Quadratic covariation estimates in non-smooth stochastic calculus," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 343-361.
    2. 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.

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