an:06162842
Zbl 1273.60046
Favetto, Benjamin
On the asymptotic variance in the central limit theorem for particle filters
EN
ESAIM, Probab. Stat. 16, 151-164 (2012).
00311580
2012
j
60G35 60F05 62M20 60J05
central limit theorem; asymptotic variance; particle filter; hidden Markov model; tightness; sequential Monte-Carlo
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.
Tom???? Cipra (Praha)