Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156259 | Stochastic Processes and their Applications | 2008 | 38 Pages |
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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Ahmed Kebaier, Arturo Kohatsu-Higa,