Hybrid multi-step estimators for stochastic differential equations based on sampled data



We consider an estimation problem of both drift and diffusion coefficient parameters for an ergodic diffusion process based on discrete observations. Hybrid multi-step estimators are proposed and their asymptotic properties, including convergence of moments, are obtained.


Adaptive estimation Bayes type estimator Convergence of moments Diffusion process Discrete time observations Maximum likelihood type estimator 

Mathematics Subject Classification

Primary 62F12 62M05 Secondary 60J60 



The authors wish to thank the referees, the associate editor the editor for their valuable comments. Kamatani’s research was partially supported by JSPS KAKENHI Grant Numbers 24740062. Uchida’s research was partially supported by JSPS KAKENHI Grant Numbers 24300107, 24654024, 25245034, and by Cooperative Research Program of the Institute of Statistical Mathematics.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Graduate School of Engineering Science and CSFIOsaka UniversityToyonakaJapan
  2. 2.CRESTJSTToyonakaJapan

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