An Ornstein-Uhlenbeck-Type Process Which Satisfies Sufficient Conditions for a Simulation-Based Filtering Procedure
In this article, we verify all the conditions stated in  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.
KeywordsInvariant Measure Transition Density Malliavin Calculus Tuning Procedure Identifiability Condition
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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