Free Access
Issue
ESAIM: PS
Volume 23, 2019
Page(s) 136 - 175
DOI https://doi.org/10.1051/ps/2018007
Published online 01 May 2019
  1. Y. Aït-Sahalia and J. Jacod, Volatility estimators for discretely sampled Lévy processes. Ann. Stat. 35 (2007) 355–392. [Google Scholar]
  2. Y. Aït-Sahalia and J. Jacod, Fisher’s information for discretely sampled Lévy processes. Econometrica 76 (2008) 727–761. [Google Scholar]
  3. O.E. Barndorff-Nielsen, T. Mikosch and S.I. Resnick (Eds.), Theory and applications, Lévy Processes. Birkhäuser Boston, Inc., Boston, MA (2001). [Google Scholar]
  4. K. Bichteler, J.-B. Gravereaux and J. Jacod, Malliavin Calculus for Processes with Jumps. Vol. 2 of Stochastics Monographs. Gordon and Breach Science Publishers, New York (1987). [Google Scholar]
  5. E. Clément and A. Gloter, Local asymptotic mixed normality property for discretely observed stochastic differential equations driven by stable Lévy processes. Stoch. Process. Appl. 125 (2015) 2316–2352. [CrossRef] [Google Scholar]
  6. E. Clément, A. Gloter and H. Nguyen, Asymptotics in Small Time for the Density of a Stochastic Differential Equation Driven by a Stable Lévy Process. Preprint HAL-01410989v2 (2017). [Google Scholar]
  7. V. Genon-Catalot and J. Jacod, On the estimation of the diffusion coefficient for multi-dimensional diffusion processes. Ann. Inst. Henri Poincaré Probab. Stat. 29 (1993) 119–151. [Google Scholar]
  8. E. Gobet, Local asymptotic mixed normality property for elliptic diffusion: a Malliavin calculus approach. Bernoulli 7 (2001) 899–912. [CrossRef] [Google Scholar]
  9. E. Gobet, LAN property for ergodic diffusions with discrete observations. Ann. Inst. Henri Poincaré Probab. Stat. 38 (2002) 711–737. [CrossRef] [MathSciNet] [Google Scholar]
  10. J. Hájek, A characterization of limiting distributions of regular estimates. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 14 (1969/1970) 323–330. [CrossRef] [Google Scholar]
  11. P. Hall and C.C. Heyde, Martingale Limit Theory and its Application. Probability and Mathematical Statistics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, London (1980). [Google Scholar]
  12. D. Ivanenko, A.M. Kulik and H. Masuda, Uniform LAN property of locally stable Lévy process observed at high frequency. ALEA Lat. Am. J. Probab. Math. Stat. 12 (2015) 835–862. [Google Scholar]
  13. J. Jacod, The Euler scheme for Lévy driven stochastic differential equations: limit theorems. Ann. Probab. 32 (2004) 1830–1872. [Google Scholar]
  14. P. Jeganathan, On the asymptotic theory of estimation when the limit of the log-likelihood ratios is mixed normal. Sankhyā Ser. A 44 (1982) 173–212. [Google Scholar]
  15. P. Jeganathan, Some asymptotic properties of risk functions when the limit of the experiment is mixed normal. Sankhyā Ser. A 45 (1983) 66–87. [Google Scholar]
  16. B.-Y. Jing, X.-B. Kong and Z. Liu, Modeling high-frequency financial data by pure jump processes. Ann. Stat. 40 (2012) 759–784. [Google Scholar]
  17. R. Kawai and H. Masuda, On the local asymptotic behavior of the likelihood function for Meixner Lévy processes under high-frequency sampling. Stat. Probab. Lett. 81 (2011) 460–469. [Google Scholar]
  18. R. Kawai and H. Masuda, Local asymptotic normality for normal inverse Gaussian Lévy processes with high-frequency sampling. ESAIM: PS 17 (2013) 13–32. [CrossRef] [EDP Sciences] [Google Scholar]
  19. V.N. Kolokoltsov, Markov Processes, Semigroups and Generators. Vol. 38 of de Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin (2011). [Google Scholar]
  20. X.-B. Kong, Z. Liu and B.-Y. Jing, Testing for pure-jump processes for high-frequency data. Ann. Stat. 43 (2015) 847–877. [Google Scholar]
  21. L. Le Cam and G.L. Yang, Asymptotics in Statistics: Some Basic Concepts. Springer Series in Statistics. Springer-Verlag, New York (1990). [CrossRef] [Google Scholar]
  22. H. Masuda, Joint estimation of discretely observed stable Lévy processes with symmetric Lévy density. J. Jpn. Stat. Soc. 39 (2009) 49–75. [CrossRef] [Google Scholar]
  23. H. Masuda, Non-Gaussian Quasi-Likelihood Estimation of sde Driven by Locally Stable Lévy Process. Preprint arXiv:1608.06758v3 (2017). [Google Scholar]
  24. J. Picard, On the existence of smooth densities for jump processes. Probab. Theory Relat. Fields 105 (1996) 481–511. [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.