  In this paper we consider an ergodic diffusion process with jumps whose drift
coefficient depends on $\mu$ and volatility coefficient depends on $\sigma$,
two unknown parameters. We suppose that the process is discretely observed at
the instants (t n i)i=0,...,n with $\Delta$n = sup i=0,...,n--1 (t n i+1 -- t n
i) $\rightarrow$ 0. We introduce an estimator of $\theta$ := ($\mu$, $\sigma$),
based on a contrast function, which is asymptotically gaussian without
requiring any conditions on the rate at which $\Delta$n $\rightarrow$ 0,
assuming a finite jump activity. This extends earlier results where a condition
on the step discretization was needed (see [13],[28]) or where only the
estimation of the drift parameter was considered (see [2]). In general
situations, our contrast function is not explicit and in practise one has to
resort to some approximation. We propose explicit approximations of the
contrast function, such that the estimation of $\theta$ is feasible under the
condition that n$\Delta$ k n $\rightarrow$ 0 where k > 0 can be arbitrarily
large. This extends the results obtained by Kessler [17] in the case of
continuous processes. Efficient drift estimation, efficient volatility
estimation,ergodic properties, high frequency data, L{\'e}vy-driven SDE,
thresholding methods.
