An optimal control variance reduction method for density estimation
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.
Volume (Year): 118 (2008)
Issue (Month): 12 (December)
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- 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.
- 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.
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