M-estimation for discretely observed ergodic diffusion processes with infinitely many jumps

Yasutaka Shimizu*

*この研究の対応する著者

研究成果: Article査読

28 被引用数 (Scopus)

抄録

We study parametric inference for multidimensional stochastic differential equations with jumps from some discrete observations. We consider a case where the structure of jumps is mainly controlled by a random measure which is generated by a Lévy process with a Lévy measure f θ(z)dz, and we admit the case f θ(z)dz=∞ in which infinitely many small jumps occur even in any finite time intervals. We propose an estimating function under this complicated situation and show the consistency and the asymptotic normality. Although the estimators in this paper are not completely efficient, the method can be applied to comparatively wide class of stochastic differential equations, and it is easy to compute the estimating equations. Therefore, it may be useful in applications. We also present some simulation results for some simple models.

本文言語English
ページ(範囲)179-225
ページ数47
ジャーナルStatistical Inference for Stochastic Processes
9
2
DOI
出版ステータスPublished - 2006 7月
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率

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