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

作者：Clement Emmanuelle^*; Delattre Sylvain; Gloter Arnaud

来源：Stochastic Processes and Their Applications, 2013, 123(7): 2500-2521.

DOI：10.1016/j.spa.2013.04.004

• LAMN property
• Convolution theorem
• Diffusion process

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.

• 出版日期2013-7