A contrast estimator for completely or partially observed hypoelliptic diffusion

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Samson, Adeline¹  Thieullen, Michele² 

[1] Univ Paris 05, PRES Sorbonne Paris Cite, Lab UMR CNRS 8145 MAP5, F-75006 Paris, France

[2] Univ Paris 06, LPMA, UMR CNRS 7599, F-75252 Paris 05, France

关键词: Hypoelliptic diffusion;    Langevin system;    Stochastic differential equations;    Partial observations;    Contrast estimator;   

DOI  :  10.1016/j.spa.2012.04.006

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free