Least squares estimators for stochastic differential equations driven by small Lévy noises

Hongwei Long, Chunhua Ma, Yasutaka Shimizu

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

We study parameter estimation for discretely observed stochastic differential equations driven by small Lévy noises. We do not impose Lipschitz condition on the dispersion coefficient function σ and any moment condition on the driving Lévy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when ε→0 and n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.

Original languageEnglish
Pages (from-to)1475-1495
Number of pages21
JournalStochastic Processes and their Applications
Volume127
Issue number5
DOIs
Publication statusPublished - 2017 May 1

Keywords

  • Asymptotic distribution
  • Consistency
  • Discrete observations
  • Least squares method
  • Parameter estimation
  • Stochastic differential equations

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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