Drift estimation on non compact support for diffusion models

Abstract We study non parametric drift estimation for an ergodic diffusion process from discrete observations. The drift is estimated on a set A using an approximate regression equation by a least squares contrast, minimized over finite dimensional subspaces of L 2 ( A , d x ) . The novelty is that the set A is non compact and the diffusion coefficient unbounded. Risk bounds of a L 2 -risk are provided where new variance terms are exhibited. A data-driven selection procedure is proposed where the dimension of the projection space is chosen within a random set contrary to usual selection procedures.

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