Invariant Density Estimation for Multidimensional Diffusions

Annamaria Bianchi ()
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Annamaria Bianchi: University of Milan, ADAMSS & Department of Mathematics

A chapter in Math Everywhere, 2007, pp 39-50 from Springer

Abstract: Abstract We consider an ℝd dimensional homogeneous diffusion process with a unique invariant density f. We construct a kernel type estimator for the invariant density and study its mean-square convergence. We find that this estimator reaches in a specific minimax sense a rate that is slower than parametric but faster than in classical d-dimensional estimation problems. Finally we examine the almost sure (pointwise and uniform) behavior of the estimator and we give examples.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-44446-6_4

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DOI: 10.1007/978-3-540-44446-6_4

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