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

@article{Kobayashi2022LeastsquaresEB,
  title={Least-squares estimators based on the Adams method for stochastic differential equations with small L{\'e}vy noise},
  author={Mitsuki Kobayashi and Yasutaka Shimizu},
  journal={Japanese Journal of Statistics and Data Science},
  year={2022}
}
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… 
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