Inference for Volatility Functionals of Itô Semimartingales Observed with Noise

This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. The estimator achieves the optimal convergence rate after explicit bias correction. A stable central limit theorem is attained with estimable asymptotic covariance matrix.