D. Applebaum, Lévy processes and 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.

Z. Q. Chen, E. Hu, L. Xie, and X. Zhang, Heat kernels for non-symmetric diffusion operators with jumps, Journal of Differential Equations, vol.263, issue.10, pp.6576-6634, 2017.

F. Comte and C. Lacour, Anisotropic adaptive kernel deconvolution, Annales de l'IHP Probabilits et statistiques, vol.49, pp.569-609, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00579608

F. Comte, C. Prieur, and A. Samson, Adaptive estimation for stochastic damping Hamiltonian systems under partial observation. Stochastic processes and their applications, vol.127, pp.3689-3718, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01659337

A. Dalalyan and M. Reiss, Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case, vol.137, p.2547, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00004828

S. Ditlevsen and P. Greenwood, The MorrisLecar neuron model embeds a leaky integrate-and-fire model, Journal of Mathematical Biology, vol.67, pp.239-259, 2013.

P. Doukhan, Mixing: properties and examples, vol.85, 2012.

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, pp.1445-1480, 2018.

A. Goldenshluger and O. Lepski, Bandwidth selection in kernel density estimation: oracle inequalities and adaptive minimax optimality, The Annals of Statistics, vol.39, issue.3, pp.1608-1632, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01265258

T. Klein and E. Rio, Concentration around the mean for maxima of empirical processes, The Annals of Probability, vol.33, issue.3, pp.1060-1077, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01979113

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

S. Kusuoka and N. Yoshida, Malliavin calculus, geometric mixing, and expansion of diffusion functionals. Probability Theory and Related Fields, vol.116, pp.457-484, 2000.

Y. A. Kutoyants, Statistical inference for ergodic diffusion processes, 2013.

C. Lacour, P. Massart, and V. Rivoirard, Estimator selection: a new method with applications to kernel density estimation, Sankhya A, vol.79, issue.2, pp.298-335, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01346081

O. Lepski, Multivariate density estimation under sup-norm loss: oracle approach, adaptation and independence structure, The Annals of Statistics, vol.41, issue.2, pp.1005-1034, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01265250

O. V. Lepski and B. Y. Levit, Adaptive non-parametric estimation of smooth multivariate functions, 1999.

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

R. C. Merton, Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, vol.3, pp.125-144, 1976.

S. P. Meyn and R. L. Tweedie, Stability of Markovian processes III: FosterLyapunov criteria for continuous-time processes, Advances in Applied Probability, vol.25, issue.3, pp.518-548, 1993.

S. M. Nikolskii, Approximation of Functions of Several Variables and Embedding Theorems, 1975.

O. Stramer and R. L. Tweedie, Existence and stability of weak solutions to stochastic differential equations with non-smooth coefficients, Statistica Sinica, pp.577-593, 1997.

C. Strauch, Adaptive invariant density estimation for ergodic diffusions over anisotropic classes, The Annals of Statistics, vol.46, issue.6B, pp.3451-3480, 2018.

A. Y. Veretennikov, Bounds for the mixing rate in the theory of stochastic equations. Theory of Probability and Its Applications, vol.32, pp.273-281, 1988.

G. Viennet, Inequalities for absolutely regular sequences: application to density estimation, Probability theory and related fields, vol.107, pp.467-492, 1997.