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On the asymptotic variance in the central limit theorem for particle filters. (English) Zbl 1273.60046
The tightness of sequence of asymptotic variances is established that are considered as functions of random observations in the framework of a hidden Markov model. The theory is applied for particle filter algorithms that approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. The behaviour of particle filters, as the number of particles increases, is asymptotically Gaussian, and the asymptotic variance in CLT depends on the the given set of observations. Examples and numerical simulations are provided.

MSC:
60G35 Signal detection and filtering (aspects of stochastic processes)
60F05 Central limit and other weak theorems
62M20 Inference from stochastic processes and prediction
60J05 Discrete-time Markov processes on general state spaces
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