Free Access
Issue
ESAIM: PS
Volume 23, 2019
Page(s) 1 - 36
DOI https://doi.org/10.1051/ps/2018004
Published online 11 March 2019
  1. L. Abbaoui and A. Bendjeddou, Exact stationary solutions for a class of nonlinear oscillators. Adv. Appl. Stat. 1 (2001) 99–106. [Google Scholar]
  2. P. Billingsley, Convergence of Probability Measures. Wiley, New York (1968). [Google Scholar]
  3. P. Cattiaux, J. León and C. Prieur, Estimation for stochastic damping hamiltonian systems under partial observations – I. Invariant density. Stoch. Process Appl. 124 (2014) 1236–1260. [CrossRef] [Google Scholar]
  4. P. Cattiaux, J. León and C. Prieur, Estimation for stochastic damping hamiltonian systems under partial observations – II Drift Term. ALEA 11 (2014) 1236–1260. [Google Scholar]
  5. V. Genon-Catalot, Maximum contrast estimation for diffusion processes from discrete observations. Statistics 21 (1990) 99–116. [Google Scholar]
  6. V. Genon-Catalot, T. Jeantheau and C. Laredo, Parameter estimation for discretely observed stochastic volatility models. Bernoulli 5 (1999) 855–872. [CrossRef] [MathSciNet] [Google Scholar]
  7. V. Genon-Catalot, T. Jeantheau and C. Laredo, Stochastic volatility models as hidden markov models and statistical applications. Bernoulli 6 (2000) 1051–1079. [CrossRef] [Google Scholar]
  8. M. Gitterman, The Noisy Oscillator: The First Hundred Years, From Einstein Until Now, 1st edn. World Scientific Publishing Co. Pte. Ltd. (2005). [CrossRef] [Google Scholar]
  9. T. Lelièvre, M. Rousset and G. Stoltz, Free Energy Computations a Mathematical Perspective. World Scientific (2010). [CrossRef] [Google Scholar]
  10. J.R. León and A. Samson, Hypoelliptic Stochastic Fitzhugh-Nagumo Neuronal Model: Mixing, Up-Crossing and Estimation of the Spike Rate. Ann. Appl. Probab. 28 (2018) 2243–2274. [Google Scholar]
  11. B. Lindner and L. Schimansky-Geier, Analytical approach to the stochastic FitzHugh-Nagumo system and coherence resonance. Phys. Rev. E 60 (1999) 7270–7276. [Google Scholar]
  12. J. Mathews and K. Fink, Numerical Methods Using MATLAB, 1st edn. Prentice Hall (1999). [Google Scholar]
  13. J. Nicolau, Nonparametric Estimation of second-order stochastic differential equations. Econ. Theory 23 (2007) 880–898. [Google Scholar]
  14. T. Ozaki, Statistical identification of nonlinear random vibration systems. J. Appl. Mech. 111 (1989) 186–191. [Google Scholar]
  15. T. Ozaki, A bridge between nonlinear time series models and nonlinear stochastic dynamical systems: a local linearization approach. Stat. Sin. 2 (1992) 113–135. [Google Scholar]
  16. Y. Pokern, A. Stuart and P. Wiberg, Parameter estimation for partially observed hypoelliptic diffusions. J. R. Stat. Soc. 71 (2009) 49–73. [CrossRef] [Google Scholar]
  17. J.B. Roberts and P.D. Spanos, Random Vibration and Statistical Linearization. Dover (2003). [Google Scholar]
  18. A. Samson and M. Thieullen, Contrast estimator for completely or partially observed hypoelliptic diffusion. Stoch. Process. Appl. 122 (2012) 2521–2552. [CrossRef] [Google Scholar]
  19. D. Talay, Stochastic hamiltonian systems:exponential convergence to the invariant measure, and discretization by the implicit euler scheme. Markov Process. Relat. Fields 8 (2002) 1–36. [Google Scholar]
  20. A. Wald, Note on the consistency of the maximum likelihood estimate. Ann. Math. Stat. 20 (1949) 595–601. [CrossRef] [Google Scholar]
  21. L. Wu, Large and moderate deviations and exponential convergence for stochastic damping hamiltonian systems. Stoch. Process. Appl. 91 (2001) 205–238. [CrossRef] [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.