On the asymptotic variance in the central limit theorem for particle filters

ESAIM - Probability and Statistics

Volumn 16, Issue , 2012, Pages 151-164

  Favetto, Benjamin ^a  

^a UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Asymptotic variance; Central Limit Theorem; Hidden Markov Model; Particle filter; Sequential Monte Carlo.; Tightness

Indexed keywords

ASYMPTOTIC VARIANCE; CENTRAL LIMIT THEOREM; MONTE CARLO; PARTICLE FILTER; TIGHTNESS;

ASYMPTOTIC ANALYSIS; DISTRIBUTED COMPUTER SYSTEMS; NONLINEAR FILTERING; TARGET TRACKING;

HIDDEN MARKOV MODELS;

EID: 84863574708     PISSN: 12928100     EISSN: 12623318     Source Type: Journal    
DOI: 10.1051/ps/2010019     Document Type: Article

References (17)

1. R. Atar and O. Zeitouni, Exponential stability for nonlinear filtering. Ann. Inst. Henri Poincaré 33 (1997) 697-725. (Pubitemid 127163500)
2. O. Cappé, E. Moulines and T. Ryden, Inference in Hidden Markov Models, in Springer Series in Statistics. Springer-Verlag New York, Inc., Secaucus, NJ, USA (2005).
3. M. Chaleyat-Maurel and V. Genon-Catalot, Computable infinite-dimensional filters with applications to discretized diffusion processes. Stoc. Proc. Appl. 116 (2006) 1447-1467. (Pubitemid 44292427)
4. N. Chopin, Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist. 32 (2004) 2385-2411. (Pubitemid 40936677)
5. E.B. Davies, Heat kernels and spectral theory, in Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge 92 (1989).
6. P. Del Moral, Feynman-Kac formulae, Genealogical and interacting particle systems with applications. Probab. Appl. Springer-Verlag, New York (2004).
7. P. Del Moral and A. Guionnet, On the stability of interacting processes with applications to filtering and genetic algorithms. Ann. Inst. Henri Poincaré 37 (2001) 155-194.
8. P. Del Moral and J. Jacod, Interacting particle filtering with discrete observations, in Sequential Monte Carlo methods in practice, Springer, New York. Stat. Eng. Inf. Sci. (2001) 43-75.
9. P. Del Moral and J. Jacod, Interacting particle filtering with discrete-time observations : asymptotic behaviour in the Gaussian case, in Stochastics in finite and infinite dimensions, Birkhäuser Boston, Boston, MA. Trends Math. (2001) 101-122.
10. R. Douc, A. Guillin and J. Najim, Moderate deviations for particle filtering. Ann. Appl. Probab. 15 (2005) 587-614. (Pubitemid 40306605)
11. R. Douc, G. Fort, E. Moulines and P. Priouret, Forgetting of the initial distribution for hidden Markov models. Stoc. Proc. Appl. 119 (2009) 1235-1256.
12. A. Doucet, N. de Freitas and N. Gordon, Sequential Monte Carlo methods in practice, Stat. Eng. Inform. Sci. Springer-Verlag, New York (2001).
13. H.R. Künsch, State space and hidden Markov models, in Complex Stochastic Systems. Eindhoven (1999); Chapman & Hall/CRC, Boca Raton, FL. Monogr. Statist. Appl. Probab. 87 (2001) 109-173.
14. H.R. Künsch, Recursive Monte Carlo filters : algorithms and theoretical analysis. Ann. Statist. 33 (2005) 1983-2021. (Pubitemid 43059668)
15. N. Oudjane and S. Rubenthaler, Stability and uniform particle approximation of nonlinear filters in case of non ergodic signals. Stoch. Anal. Appl. 23 (2005) 421-448. (Pubitemid 40801686)
16. C.P. Robert and G. Casella, Monte Carlo statistical methods, 2nd edition, in Springer Texts in Statistics. Springer-Verlag, New York (2004).
17. R. Van Handel, Uniform time average consistency of Monte Carlo particle filters. Stoc. Proc. Appl. 119 (2009) 3835-3861.