## Twisted particle filters.(English)Zbl 1302.60139

The authors introduce the so-called hidden Markov model (HMM) which operates as a Markov chain on a measurable space $$X$$ and yields values on a suitable observation space $$Y$$; for each $$X_n$$, the value $$Y_n$$ is conditionally independent on the rest of the process, given $$X_n$$. The model is considered for the $$N$$-particle sytems. The simplest particle filter, known as the bootstrap algorithm, is a departure point for further introduction and discussion of more elaborate filters, with a focus on the $$N\rightarrow \infty$$ regime. The main purpose of the present paper is to rigorously address comparative issues of how and why one algorithm may outperform another, and how it is possible to modify standard algorithms in order to improve performance. To this end, the twisted particle filters are introduced and validated by means of a traditional asymptotic analysis, in the regime where the number of particles tends to infinity.

### MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory 62M20 Inference from stochastic processes and prediction 60G35 Signal detection and filtering (aspects of stochastic processes)
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### References:

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