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An Ornstein-Uhlenbeck-Type Process Which Satisfies Sufficient Conditions for a Simulation-Based Filtering Procedure

  • Arturo Kohatsu-HigaEmail author
  • Kazuhiro Yasuda
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)

Abstract

In this article, we verify all the conditions stated in [8] in order for a filtering/estimation procedure based on Monte Carlo simulations of unknown densities of diffusion processes to converge to its theoretical values. In order to verify these hypotheses one needs to use extensively various properties of the diffusion processes and its Euler–Maruyama approximation. In particular, we need to study flow properties, upper and lower bounds for densities and existence of invariant measures and α-mixing properties.

As a consequence one obtains that there is a tuning procedure which chooses the number of steps in the Euler–Maruyama scheme, the window size of the kernel estimation method and the Monte Carlo simulation size in function of the number of available data.

Keywords

Invariant Measure Transition Density Malliavin Calculus Tuning Procedure Identifiability Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This research was supported by grants from the Japan Ministry of Education and Science and the Japan Science and Technology Agency. The authors would like to thank all the people that gave us information about related results.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesRitsumeikan UniversityKyotoJapan
  2. 2.Japan Science and Technology AgencyTokyoJapan
  3. 3.Faculty of Science and EngineeringHosei UniversityTokyoJapan

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