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Recursive estimation for stochastic damping hamiltonian systems

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  • P. Cattiaux
  • José R. León
  • C. Prieur

Abstract

In this paper, we complete our previous works on the nonparametric estimation of the characteristics (invariant density, drift term, variance term) of some ergodic hamiltonian systems, under partial observations. More precisely, we introduce recursive estimators using the full strength of the ergodic behaviour of the underlying process. We compare the theoretical properties of these estimators with the ones of the estimators we previously introduced in Cattiaux, Leon and Prieur ['Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. I. Invariant Density', Stochastic Processes and their Application , 124(3):1236-1260; 'Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. II. Drift term', ALEA Latin American Journal of Probability and Mathematical Statistics , 11, 359-384; 'Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. III. Diffusion term,' http://hal.archives-ouvertes.fr/hal-01044611.

Suggested Citation

  • P. Cattiaux & José R. León & C. Prieur, 2015. "Recursive estimation for stochastic damping hamiltonian systems," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 401-424, September.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:401-424
    DOI: 10.1080/10485252.2015.1046451
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    References listed on IDEAS

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    1. Han-Ying Liang & Jong-Il Baek, 2004. "Asymptotic normality of recursive density estimates under some dependence assumptions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 155-166, September.
    2. Masry, Elias, 1989. "Nonparametric estimation of conditional probability densities and expectations of stationary processes: strong consistency and rates," Stochastic Processes and their Applications, Elsevier, vol. 32(1), pages 109-127, June.
    3. Masry, Elias & Györfi, László, 1987. "Strong consistency and rates for recursive probability density estimators of stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 79-93, June.
    4. Masry, Elias, 1987. "Almost sure convergence of recursive density estimators for stationary mixing processes," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 249-254, June.
    5. Wu, Liming, 2001. "Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 205-238, February.
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