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Statistics on crossings of discretized diffusions and local time

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  • Florens-Zmirou, D.

Abstract

Let X[Delta] be the process obtained by linear interpolation from discrete observations of a diffusion X. In the first part of this paper we study the statistical properties of the observation sgn X[Delta]. In the second part we prove that the number of zero-crossings of X[Delta], suitably normalized, converges in (L2-norm) to the zero local time of X.

Suggested Citation

  • Florens-Zmirou, D., 1991. "Statistics on crossings of discretized diffusions and local time," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 139-151, October.
    • Handle: RePEc:eee:spapps:v:39:y:1991:i:1:p:139-151
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    Cited by:

    1. Emmanuel Gobet & Gustaw Matulewicz, 2017. "Parameter estimation of Ornstein–Uhlenbeck process generating a stochastic graph," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 211-235, July.

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