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

Mitsuki Kobayashi*, Yasutaka Shimizu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)217-240
Number of pages24
JournalJapanese Journal of Statistics and Data Science
Volume5
Issue number1
DOIs
Publication statusPublished - 2022 Jul

Keywords

  • Asymptotic distribution
  • Discrete observations
  • SDE driven by Lévy noise
  • Small noise asymptotics
  • The Adams method

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Theory and Mathematics

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