Y. Aït-sahalia and J. Yu, Saddlepoint Approximations for Continuous-Time Markov Processes, Journal of Econometrics, vol.134, pp.507-551, 2006.

D. L. Applebaum, processes, & stochastic calculus, 2009.

O. E. Barndorff-nielsen and N. Shephard, Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Financial Economics, J. R. Stat. Soc., Ser. B, Stat. Methodol, vol.63, pp.167-241, 2001.

D. S. Bates, Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark, The Review of Financial Studies, vol.9, issue.1, pp.69-107, 1996.

K. Bichteler, Malliavin calculus for processes with jumps, Stochastics Monographs, 1987.

S. Ditlevsen and P. Greenwood, The Morris-lecar Neuron Model Embeds a Leaky Integrate-AndFire Model, Journal of Mathematical Biology, vol.67, pp.239-259, 2013.

B. Eraker, M. Johannes, and P. &-n, The Impact of Jumps in Volatility and Returns, J. Finance, vol.58, issue.3, p.1269, 2003.

F. Zmirou and D. , Approximate discrete-time schemes for statistics of diffusion processes, Statistics: A Journal of Theoretical and Applied Statistics, vol.20, pp.547-557, 1989.

G. Catalot, V. Jacod, and J. , On the estimation of the diffusion coefficient for multi-dimensional diffusion processes. Annales de l'institut Henri Poincaré (B) Probabilités et Statistiques, vol.29, pp.119-151, 1993.

A. Gloter, D. Loukianova, and H. Mai, Jump Filtering and Efficient Drift Estimation for Lévy-Driven Sdes, The Annals of Statistics, vol.46, issue.4, p.1445, 2018.

I. A. Ibragimov and R. Z. Has'-minskii, Statistical Estimation: Asymptotic Theory, vol.16, 2013.

J. Jacod and P. Protter, Discretization of Processes, vol.67, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00103988

J. Jacod and A. Shiryaev, Limit theorems for stochastic processes, vol.288, 2013.

N. Jakobsen and M. Sørensen, Estimating Functions for Jump-Diffusions, 2017.

M. Kessler, Estimation of an Ergodic Diffusion from Discrete Observations, Scandinavian Journal of Statistics, vol.24, issue.2, pp.211-229, 1997.

S. G. Kou, A Jump Diffusion Model for Option Pricing, Management Science, vol.48, pp.1086-1101, 2002.

C. Li and D. Chen, Estimating Jump-Diffusions Using Closed Form Likelihood Expansions, Journal of Econometrics, vol.195, pp.51-71, 2016.

H. Masuda, Ergodicity and exponential beta mixing bounds for multidimensional diffusions with jumps. Stochastic processes and their applications, vol.117, pp.35-56, 2007.

H. Masuda, Erratum to: Ergodicity and exponential beta mixing bound for multidimensional diffusions with jumps, Stochastic Processes and their Applications, vol.117, pp.676-678, 2007.

H. Masuda, Convergence of Gaussian Quasi-Likelihood Random Fields for Ergodic Lévy Driven Sde Observed At High Frequency, Annals of Stat, vol.41, issue.3, p.1593, 2013.

R. C. Merton, Option Pricing When Underlying Stock Returns Are Discontinuous, Journal of Financial Economics, vol.3, pp.125-144, 1976.

S. M. Nikolskii, Approximation of Functions of Several Variables and Imbedding Theorems (russian). Sec. Ed., Moskva, Nauka 1977 English Translation of the First Ed, 1975.

P. E. Protter, Stochastic differential equations, Stochastic integration and differential equations, pp.249-361, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00101949

Y. Shimizu, M Estimation for Discretely Observed Ergodic Diffusion Processes with Infinitely many Jumps. Statistical Inference for Stochastic Processes, vol.9, pp.179-225, 2006.

Y. Shimizu and N. Yoshida, Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations. Statistical Inference for Stochastic Processes, vol.9, pp.227-277, 2006.

N. Yoshida, Estimation for Diffusion Processes from Discrete Observation, Journal of Multivariate Analysis, vol.41, pp.220-242, 1992.

U. Lamme and . Cnrs, , p.8071

, mail: arnaud.gloter@univ-evry.fr that converges to 0 in norm L 1 (and therefore in probability) since > 0 and n? n ? ? for n ? ?. Concerning the second term of (219), using Burkholder-Davis-Gundy inequality and (215) we have Concerning the set E h ? N i n , we use Markov inequality and we obtain