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