A sequential particle algorithm that keeps the particle system alive

Lecture Notes in Control and Information Sciences

Volumn 337, Issue , 2006, Pages 351-389

  LeGland, François ^a   Oudjane, Nadia ^b,c  

^a CAMPUS DE BEAULIEU   (France)

^b EDF R AND D   (France)

^c UNIVERSITÉ PARIS 13   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; CONTROL; SOFTWARE ENGINEERING;

CENTRAL LIMIT THEOREM; IMPORTANCE SPLITTING; INDEPENDENT RANDOM VARIABLES; PARTICLE SYSTEMS; RANDOM NUMBERS; SELECTION FUNCTION; TRIANGULAR ARRAYS; ZERO VALUES;

RANDOM NUMBER GENERATION;

EID: 33947674148     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/11587392_11     Document Type: Article

References (20)

1. Frédéric Cérou, Pierre Del Moral, François Le Gland, and Pascal Lezaud. Limit theorems for the multilevel splitting algorithm in the simulation of rare events. In Michael E. Kuhl, Natalie M. Steiger, Frank B. Armstrong, and Jeffrey A. Joines, editors, Proceedings of the 2005 Winter Simulation Conference, Orlando 2005, December 2005.
2. Didier Dacunha-Castelle and Marie Duflo. Probability and Statistics II. Springer-Verlag, Berlin, 1986.
3. Pierre Del Moral. Feynman-Kac Formulae. Genealogical and Interacting Particle Systems with Applications. Probability and its Applications. Springer-Verlag, New York, 2004.
4. Pierre Del Moral and Jean Jacod. Interacting particle filtering with discrete observations. In Arnaud Doucet, Nando de Freitas, and Neil Gordon, editors, Sequential Monte Carlo Methods in Practice, Statistics for Engineering and Information Science, chapter 3, pages 43-75. Springer-Verlag, New York, 2001.
5. Pierre Del Moral, Jean Jacod, and Philip Protter. The Monte Carlo method for filtering with discrete-time observations. Probability Theory and Related Fields, 120(3):346-368, 2001.
6. Pierre Del Moral and Pascal Lezaud. Branching and interacting particle interpretation of rare event probabilities. In Henk Blom and John Lygeros, editors, Stochastic Hybrid Systems : Theory and Safety Critical Applications, Lecture Notes in Control and Information Sciences, chapter 14. Springer-Verlag, Berlin. To appear.
7. Pierre Del Moral and Laurent Miclo. Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to nonlinear filtering. In Jacques Azéma, Michel Émery, Michel Ledoux, and Marc Yor, editors, Séminaire de Probabilités XXXIV, volume 1729 of Lecture Notes in Mathematics, pages 1-145. Springer-Verlag, Berlin, 2000.
8. Allan Gut. Stopped Random Walks. Limit Theorems and Applications. Applied Probability (A Series of the Applied Probability Trust). Springer-Verlag, New York, 1988.
9. Hans R. Künsch. Recursive Monte Carlo filters : Algorithms and theoretical analysis. The Annals of Statistics, 33(5):1983-2021, October 2005.
10. François Le Gland and Nadia Oudjane. A robustification approach to stability and to uniform particle approximation of nonlinear filters : the example of pseudo-mixing signals. Stochastic Processes and their Applications, 106(2):279-316, August 2003.
11. François Le Gland and Nadia Oudjane. Stability and uniform approximation of nonlinear filters using the Hilbert metric, and application to particle filters. The Annals of Applied Probability, 14(1):144-187, February 2004.
12. François Le Gland and Nadia Oudjane. A sequential particle algorithm that keeps the particle system alive. In Proceedings of the 13th European Signal Processing Conference, Antalya 2005. EURASIP, September 2005.
13. François Le Gland and Nadia Oudjane. A sequential algorithm that keeps the particle system alive. Rapport de Recherche 582G, INRIA, February 2006. ftp: //ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5826.pdf.
14. Jacques Neveu. Discrete-Parameter Martingales, volume 10 of North-Holland Mathematical Library. North-Holland, Amsterdam, 1975.
15. Nadia Oudjane. Stabilité et Approximations Particulaires en Filtrage Non-Linéaire - Application au Pistage. Thèse de Doctorat, Université de Rennes 1, Rennes, December 2000. ftp://ftp.irisa.fr/techreports/theses/2000/oudjane.pdf.
16. Nadia Oudjane and Sylvain Rubenthaler. Stability and uniform particle approximation of nonlinear filters in case of non ergodic signal. Stochastic Analysis and Applications, 23(3):421-448, May 2005.
17. Alfréd Rényi. On the asymptotic distribution of the sum of a random number of independent random variables. Acta Mathematica Academiae Scientiarum Hungaricae, 8:193-199, 1957.
18. Vivien Rossi. Filtrage Non-Linéaire par Noyaux de Convolution - Application à un Procédé de Dépollution Biologique. Thèse de Doctorat, École Nationale Supérieure Agronomique de Montpellier, Montpellier, December 2004.
19. Vivien Rossi and Jean-Pierre Vila. Nonlinear filtering in discrete time : A particle convolution approach. Statistical Inference for Stochastic Processes. To appear.
20. David Siegmund. Sequential Analysis. Tests and Confidence Intervals. Springer Series in Statistics. Springer-Verlag, New York, 1985.