EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 26 (2022) ESAIM: PS, 26 (2022) 126-151 References
Open Access
Issue
ESAIM: PS
Volume 26, 2022
Page(s) 126 - 151
DOI https://doi.org/10.1051/ps/2022001
Published online 01 February 2022
  1. C. Amorino and A. Gloter, Invariant density adaptive estimation for ergodic jump diffusion processes over anisotropic classes. J. Stat. Plan. Inference 213 (2021) 106–129. [CrossRef] [Google Scholar]
  2. C. Amorino, Rate of estimation for the stationary distribution of jump-processes over anisotropic Hölder classes. To appear Electr. J. Stat. (2022). [Google Scholar]
  3. C. Amorino, C. Dion, A. Gloter and S. Lemler, On the nonparametric inference of coefficients of self-exciting jump-diffusion. Preprint arXiv:2011.12387 (2020). [Google Scholar]
  4. D. Applebaum, Lévy processes and stochastic calculus. Cambridge University Press (2009). [CrossRef] [Google Scholar]
  5. G. Banon, Nonparametric identification for diffusion processes. SIAM J. Control Optim. 16 (1978) 380–395. [CrossRef] [MathSciNet] [Google Scholar]
  6. G. Banon and H.T. Nguyen, Recursive estimation in diffusion model. SIAM J. Control Optim. 19 (1981) 676–685. [CrossRef] [MathSciNet] [Google Scholar]
  7. 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. 63 (2001) 167–241. [CrossRef] [MathSciNet] [Google Scholar]
  8. D. Blanke, Estimation de la densité pour des trajectoires non directement observables. Publ. Inst. Statist. Univ. Paris 40 (1996) 21–36. [MathSciNet] [Google Scholar]
  9. D. Bosq, Parametric rates of nonparametric estimators and predictors for continuous time processes. Ann. Statist. 25 (1997) 982–1000. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. Bosq, Nonparametric Statistics for Stochastic Processes (Second edition), Lecture Notes Statist., 110. Springer-Verlag, New York (1998). [CrossRef] [Google Scholar]
  11. D. Bosq, Minimax rates of density estimators for continuous time processes. Sankhya. Ser. A 60 (1998) 18–28. [MathSciNet] [Google Scholar]
  12. D. Bosq and Yu. Davydov, Local time and density estimation in continuous time. Math. Methods Stat. 8 (1999) 22–45. [Google Scholar]
  13. D. Bosq, F. de Merlevè and M. Peligrad, Asymptotic normality for density kernel estimators in discrete and continuous time. J. Multivar. Anal. 68 (1999) 78–95. [CrossRef] [Google Scholar]
  14. J.V. Castellana and M.R. Leadbetter, On smoothed probability density estimation for stationary processes. Stoch. Process Appl. 21 (1986) 179–193. [CrossRef] [Google Scholar]
  15. Z.Q. Chen, E. Hu, L. Xie and X. Zhang, Heat kernels for non-symmetric diffusion operators with jumps. J Differ Equ. 263 (2017) 6576–6634. [CrossRef] [Google Scholar]
  16. N. Cheze-Payaud, Nonparametric regression and prediction for continuous-time processes. Publ. Inst. Statist. Univ. Paris 38 (1994) 37–58. [MathSciNet] [Google Scholar]
  17. F. Comte and C. Lacour, Anisotropic adaptive kernel deconvolution. Ann. Inst. Henri Poincaré, Probab. Statis. 49 (2013) 569–609. [Google Scholar]
  18. F. Comte and F. Merlevède, Super optimal rates for nonparametric density estimation via projection estimators. Stoch. Process Appl. 115 (2005) 797–826. [CrossRef] [Google Scholar]
  19. S. Delattre, A. Gloter and N. Yoshida, Rate of Estimation for the Stationary Distribution of Stochastic Damping Hamiltonian Systems with Continuous Observations. Preprint arXiv:2001.10423 (2020). [Google Scholar]
  20. M. Delecroix, Sur l’estimation des densités d’un processus stationnaire á temps continu. Publications de l’ISUP XXV (1980) 17–39. [Google Scholar]
  21. Y.A. Kutoyants, Efficient density estimation for ergodic diffusion processes. Stat. Inference Stoch. Process. 1 (1998) 131–155. [CrossRef] [MathSciNet] [Google Scholar]
  22. N. Dexheimer, C. Strauch and L. Trottner, Mixing it up: A general framework for Markovian statistics beyond reversibility and the minimax paradigm. Preprint arXiv:2011.00308 (2020). [Google Scholar]
  23. C. Dion and S. Lemler, Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process. Stat. Inference Stochastic Processes 23 (2020) 489–515. [CrossRef] [MathSciNet] [Google Scholar]
  24. S. Ditlevsen and P. Greenwood, The Morris–Lecar neuron model embeds a leaky integrate-and-fire model. J. Math. Biol. 67 (2013) 239–259. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  25. P. Doukhan, Mixing: properties and examples Vol. 85. Springer Science and Business Media (2012). [Google Scholar]
  26. A. Friedman, Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, N.J. (1964). [Google Scholar]
  27. B. Funke and E. Schmisser, Adaptive nonparametric drift estimation of an integrated jump diffusion process. ESAIM: PS 22 (2018) 236–260. [CrossRef] [EDP Sciences] [Google Scholar]
  28. R.Z. Has’minskii, Stability of differential equations. Sijthoff and Noordhoff, Germantown, MD (1980). [CrossRef] [Google Scholar]
  29. R. Höpfner, M. Hoffmann and E. Löcherbach, Non-parametric estimation of the death rate in branching diffusions. Scand. J. Stat. 29 (2002) 665–692. [CrossRef] [Google Scholar]
  30. A. Juditsky and A. Nemirovski, On nonparametric tests of positivity/monotonicity/convexity. Ann. Stat. (2002) 498–527. [Google Scholar]
  31. S.G. Kou, A jump-diffusion model for option pricing. Manag. Sci. 48 (2002) 1086–1101. [CrossRef] [Google Scholar]
  32. Y.A. Kutoyants, Some problems of nonparametric estimation by observations of ergodic diffusion process. Statist. Probab. Lett. 32 (1997) 311–320. [CrossRef] [MathSciNet] [Google Scholar]
  33. D. Lamberton and G. Pages, Recursive computation of the invariant distribution of a diffusion. Bernoulli 8 (2002) 367–405. [MathSciNet] [Google Scholar]
  34. F. Leblanc, Density estimation for a class of continuous time processes. Math. Methods Stat. 6 (1997) 171–199. [Google Scholar]
  35. O.V. Lepski and V.G. Spokoiny, Optimal pointwise adaptive methods in nonparametric estimation. Ann. Stat. (1997) 2512–2546. [Google Scholar]
  36. H. Masuda, Ergodicity and exponential beta - mixing bounds for multidimensional diffusions with jumps. Stoch. Process. Appl. 117 (2007) 35–56. [CrossRef] [Google Scholar]
  37. R.C. Merton, Option pricing when underlying stock returns are discontinuous. J. Financ. Econ. 3 (1976) 125–144. [CrossRef] [Google Scholar]
  38. H.T. Nguyen, Density estimation in a continuous-time Markov processes. Ann. Statist. 7 (1979) 341–348. [CrossRef] [MathSciNet] [Google Scholar]
  39. F. Panloup, Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process. Ann. Appl. Probab. 18 (2008) 379–426. [CrossRef] [MathSciNet] [Google Scholar]
  40. E. Schmisser, Non parametric estimation of the diffusion coefficients of a diffusion with jumps. Stoch. Process. Appl. 129 (2019) 5364–5405. [CrossRef] [Google Scholar]
  41. C. Strauch, Adaptive invariant density estimation for ergodic diffusions over anisotropic classes. Ann. Stat. 46 (2018) 3451–3480. [CrossRef] [Google Scholar]
  42. A.B. Tsybakov, On nonparametric estimation of density level sets. Ann. Stat. 25 (1997) 948–969. [CrossRef] [Google Scholar]
  43. A.B. Tsybakov, Introduction to nonparametric estimation. Springer Science and Business Media (2008). [Google Scholar]
  44. H. Van Zanten, Rates of convergence and asymptotic normality of kernel estimators for ergodic diffusion processes. Nonparametric Statist. 13 (2001) 833–850. [CrossRef] [MathSciNet] [Google Scholar]
  45. A.Yu. Veretennikov, On Castellana-Leadbetter’s condition for diffusion density estimation. Stat. Inference Stoch. Process. 2 (1999) 1–9. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.