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An optimal control variance reduction method for density estimation

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  • Kebaier, Ahmed
  • Kohatsu-Higa, Arturo

Abstract

We study the problem of density estimation of a non-degenerate diffusion using kernel functions. Thanks to Malliavin calculus techniques, we obtain an expansion of the discretization error. Then, we introduce a new control variate method in order to reduce the variance in the density estimation. We prove a stable law convergence theorem of the type obtained in Jacod-Kurtz-Protter for the first Malliavin derivative of the error process, which leads us to get a CLT for the new control variate algorithm. This CLT gives us a precise description of the optimal parameters of the method.

Suggested Citation

  • Kebaier, Ahmed & Kohatsu-Higa, Arturo, 2008. "An optimal control variance reduction method for density estimation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2143-2180, December.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:12:p:2143-2180
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    References listed on IDEAS

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    1. Arturo Kohatsu & Roger Pettersson, 2002. "Variance reduction methods for simulation of densities on Wiener space," Economics Working Papers 597, Department of Economics and Business, Universitat Pompeu Fabra.
    2. BALLY Vlad & TALAY Denis, 1996. "The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density," Monte Carlo Methods and Applications, De Gruyter, vol. 2(2), pages 93-128, December.
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    Cited by:

    1. Delong, Lukasz & Imkeller, Peter, 2010. "On Malliavin's differentiability of BSDEs with time delayed generators driven by Brownian motions and Poisson random measures," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1748-1775, August.

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