期刊
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
卷 122, 期 7, 页码 2521-2552出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.spa.2012.04.006
关键词
Hypoelliptic diffusion; Langevin system; Stochastic differential equations; Partial observations; Contrast estimator
资金
- Agence Nationale de la Recherche [ANR-09-BLAN-0008-01]
- Agence Nationale de la Recherche (ANR) [ANR-09-BLAN-0008] Funding Source: Agence Nationale de la Recherche (ANR)
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.
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