Abstract
We propose punctual and functional estimators for the local variance of pseudo-diffusions driven by Gaussian noises. The consistency and asymptotic normality are shown. The proofs are simplified by using the Central Limit Theorem for non-linear functionals belonging to Itô-Wiener’s Chaos, of Peccati-Nualart-Tudor. Besides, a simulation study is made to assess the performance of those estimators. This study reveals, through various examples, that the estimators give good approximations for the true local variance.
Citation
Corinne Berzin. Alain Latour. José R. León. "Variance estimator for fractional diffusions with variance and drift depending on time." Electron. J. Statist. 9 (1) 926 - 1016, 2015. https://doi.org/10.1214/15-EJS1023
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