Estimation of state-dependent jump activity and drift for Markovian semimartingales

The jump behavior of an infinitely active Itô semimartingale can be conveniently characterized by a activity index Blumenthal–Getoor type, typically assumed to constant in time. We study Markovian semimartingales with non-constant, state-dependent and non-vanishing continuous diffusion component. A nonparametric estimator for the functional is proposed shown asymptotically normal under combined high-frequency long-time-span asymptotics. Furthermore, we propose drift which robust symmetric jumps infinite variance variation, attains same asymptotic as process. Simulations demonstrate finite sample our estimators. mathematical results are based on novel uniform bound Markov generator diffusion.