Least-squares estimators based on the Adams method for stochastic differential equations with small Lévy noise

Mitsuki Kobayashi*, Yasutaka Shimizu

*この研究の対応する著者

研究成果: Article査読

抄録

We consider stochastic differential equations (SDEs) driven by small Lévy noise with some unknown parameters and propose a new type of least-squares estimators based on discrete samples from the SDEs. To approximate the increments of a process from the SDEs, we shall use not the usual Euler method but the Adams method, that is, a well-known numerical approximation of the solution to the ordinary differential equation appearing in the limit of the SDE. We show the consistency of the proposed estimators and the asymptotic distribution in a suitable observation scheme. We also show that our estimators can be better than the usual LSE based on the Euler method in the finite sample performance.

本文言語English
ページ(範囲)217-240
ページ数24
ジャーナルJapanese Journal of Statistics and Data Science
5
1
DOI
出版ステータスPublished - 2022 7月

ASJC Scopus subject areas

  • 統計学および確率
  • 計算理論と計算数学

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