An infinite dimensional convolution theorem with applications to the efficient estimation of the integrated volatility

Abstract : This paper proposes a general approach to obtain asymptotic lower bounds for the estimation of random functionals. The main result is an abstract convolution theorem in a non parametric setting, based on an associated LAMN property. This result is then applied to the estimation of the integrated volatility, or related quantities, of a diffusion process, when the diffusion coefficient depends on an independent Brownian motion.
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Submitted on : Thursday, July 19, 2012 - 7:36:06 PM
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Emmanuelle Clement, Sylvain Delattre, Arnaud Gloter. An infinite dimensional convolution theorem with applications to the efficient estimation of the integrated volatility. Stochastic Processes and their Applications, Elsevier, 2013, 123, pp.2500-2521. ⟨hal-00719460⟩

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