  In this paper, we present the double smoothed nonparametric approach for
infinitesimal conditional volatility of jump-diffusion model based on high
frequency data. Under certain minimal conditions, we obtain the strong
consistency and asymptotic normality for the estimator as the time span $T
\rightarrow \infty$ and the sample interval $\Delta_{n} \rightarrow 0.$ The
procedure and asymptotic behavior can be applied for both null Harris recurrent
and positive Harris recurrent processes.
