Recursive estimation for stochastic damping hamiltonian systems

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].

Keywords:

• hypoelliptic diffusion
• nonparametric estimation
• recursive estimation
• partial observations

AMS Subject Classification:

• 62G07
• 60H10
• 60F05

Disclosure statement

No potential conflict of interest was reported by the authors.