Least squares estimators for discretely observed stochastic processes driven by small Lévy noises

Hongwei Long*, Yasutaka Shimizu, Wei Sun

*この研究の対応する著者

研究成果査読

36 被引用数 (Scopus)

抄録

We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of convergence of the least squares estimator (LSE) of the drift parameter when a small dispersion coefficient ε → 0 and n → ∞ simultaneously. The asymptotic distribution of the LSE in our general setting is shown to be the convolution of a normal distribution and a distribution related to the jump part of the Lévy process. Moreover, we briefly remark that our methodology can be easily extended to the more general case of semi-martingale noises.

本文言語English
ページ(範囲)422-439
ページ数18
ジャーナルJournal of Multivariate Analysis
116
DOI
出版ステータスPublished - 2013 4
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • 数値解析
  • 統計学、確率および不確実性

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