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Strong Consistency of the Bayesian Estimator for the Ornstein–Uhlenbeck Process

In: Inspired by Finance

Author

Listed:
  • Arturo Kohatsu-Higa

    (Ritsumeikan University and Japan Science and Technology Agency)

  • Nicolas Vayatis

    (École Normale Supérieure de Cachan, Centre de Mathématiques et de Leurs Applications (CMLA) UMR CNRS 8536)

  • Kazuhiro Yasuda

    (Hosei University)

Abstract

In the accompanying paper Kohatsu-Higa et al. (submitted, 2013), we have done a theoretical study of the consistency of a computational intensive parameter estimation method for Markovian models. This method could be considered as an approximate Bayesian estimator method or a filtering problem approximated using particle methods. We showed in Kohatsu-Higa (submitted, 2013) that under certain conditions, which explicitly relate the number of data, the amount of simulations and the size of the kernel window, one obtains the rate of convergence of the method. In this first study, the conditions do not seem easy to verify and for this reason, we show in this paper how to verify these conditions in the toy example of the Ornstein–Uhlenbeck processes. We hope that this article will help the reader understand the theoretical background of our previous studies and how to interpret the required hypotheses.

Suggested Citation

  • Arturo Kohatsu-Higa & Nicolas Vayatis & Kazuhiro Yasuda, 2014. "Strong Consistency of the Bayesian Estimator for the Ornstein–Uhlenbeck Process," Springer Books, in: Yuri Kabanov & Marek Rutkowski & Thaleia Zariphopoulou (ed.), Inspired by Finance, edition 127, pages 411-437, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-02069-3_19
    DOI: 10.1007/978-3-319-02069-3_19
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