A contrast estimator for completely or partially observed hypoelliptic diffusion |
| |
Authors: | Adeline Samson Michèle Thieullen |
| |
Institution: | 1. PRES Sorbonne Paris Cité, Université Paris Descartes, Laboratoire MAP5 UMR CNRS 8145, 45 rue des St Pères, 75006 Paris, France;2. Université Pierre et Marie Curie - Paris 6, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), UMR CNRS 7599, Boîte 188, 4, Place Jussieu, 75252 Paris cedex 05, France |
| |
Abstract: | Parametric estimation of two-dimensional hypoelliptic diffusions is considered when complete observations–both coordinates discretely observed–or partial observations–only one coordinate observed–are available. Since the volatility matrix is degenerate, Euler contrast estimators cannot be used directly. For complete observations, we introduce an Euler contrast based on the second coordinate only. For partial observations, we define a contrast based on an integrated diffusion resulting from a transformation of the original one. A theoretical study proves that the estimators are consistent and asymptotically Gaussian. A numerical application to Langevin systems illustrates the nice properties of both complete and partial observations’ estimators. |
| |
Keywords: | Hypoelliptic diffusion Langevin system Stochastic differential equations Partial observations Contrast estimator |
本文献已被 ScienceDirect 等数据库收录! |
|