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- 2Law of large numbers
- 2Particle filters
- 1Duncan–Mortensen–Zakai equation
- 1Functional central limit theorem
- 1Functional law of the iterated logarithms
- 1Large deviations principle
The classical particle filter, introduced in 1993, approximates the normalized filter directly. It has two defiencies, over resampling and the inability to distinguish models, the former of which was overcome but the later is fundamental. Conversely, the weighted particle filter, motivated by the...
Herein, we consider direct Markov chain approximations to the Duncan–Mortensen–Zakai equations for nonlinear filtering problems on regular, bounded domains. For clarity of presentation, we restrict our attention to reflecting diffusion signals with symmetrizable generators. Our Markov chains are...