• Corpus ID: 18121590

A Branching Particle Approximation to the Filtering Problem with Counting Process Observations ∗

@inproceedings{Xiong2006ABP,
  title={A Branching Particle Approximation to the Filtering Problem with Counting Process Observations ∗},
  author={Jie Xiong and Yong Zeng},
  year={2006}
}

• J. Xiong, Yong Zeng
• Published 2006
• Mathematics

Recently, the filtering model with counting process observations has been demonstrated as a sensible framework for modeling the micromovement of asset price (or ultra-high frequency data). In this paper, we first construct a branching particle system for such a nonlinear filtering model. Then, we show the weighted empirical measures in the constructed branching system converges to the optimal filters uniformly in time by deriving sharp upper bounds for the mean square error. Furthermore, we prove a central limit type theorem to characterize the convergence rate of such weighted empirical measures. The convergence rate is n, which is better than the best rate in the classical nonlinear filtering case where the rate is n(1−α)/2 for any α > 0. 2000 Mathematics Subject Classification. Primary: 60H15; Secondary: 60K35, 35R60, 93E11, 60F05, 91B28.