Branching and interacting particle interpretations of rare event probabilities

Lecture Notes in Control and Information Sciences

Volumn 337, Issue , 2006, Pages 277-323

  Del Moral, Pierre ^a   Lezaud, Pascal ^b  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

^b Cent d'Etudes de la Navigation   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; MONTE CARLO METHODS;

ASYMPTOTIC THEORIES; CENTRAL LIMIT THEOREM; ESTIMATION PROBLEM; EXTINCTION PROBABILITY; INTERACTING PARTICLES; INTERACTING-PARTICLE ALGORITHMS; PARTICLE TRAPPING; RARE EVENT PROBABILITIES;

IMPORTANCE SAMPLING;

EID: 33947694624     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (16)

1. F. Cérou, P. Del Moral, F. LeGland, and P. Lezaud. Genetic Genealogical Models in Rare Events Analysis. Publication du Laboratoire de Statistique et Probabilités, Toulouse III, 2002.
2. P. Del Moral. Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Springer-Verlag, 2004.
3. P. Del Moral and J. Jacod. Interacting Particle Filtering With Discrete Observations. In A. Doucet, N. de Freitas, and N. Gordon, editors, Sequential Monte Carlo Methods in Practice. Springer Verlag, 2001.
4. P. Del Moral and L. Miclo. Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering. In J. Azma, M. Émery, M. Ledoux, and M. Yor, editors, Séminaire de Probabilités XXXIV, volume 1729 of Lecture Notes in Mathematics, pages 1-14. Springer, 2000.
5. P. Del Moral and L. Miclo. Particle Approximations of Lyapunov Exponents Connected to Schrödinger Operators and Feynman-Kac Semigroups. ESAIM: Probability and Statistics, 7:171-208, 2003.
6. A. Doucet, N. de Freitas, and N. Gordon. An Introduction to Sequential Monte Carlo Methods. In A. Doucet, N. de Freitas, and N. Gordon, editors, Sequential Monte Carlo Methods in Practice. Springer Verlag, 2001.
7. P. Embrechts, C. Klüppelberg, and T. Mikosch. Modelling Extremal Events for Insurance and Finance. Springer, 2003.
8. T.E. Harris and H. Kahn. Estimation of particle transmission by random sampling. Nail. Bur. Stand. Appl. Math. Ser., 12:27-30, 1951.
9. J. Krystul and H. Blom. Sequential Monte Carlo Simulation of Rare Event Probability. Hybridge report D9.3, http://www.nlr.nl/public/hosted-sites/ hybridge/, 2004.
10. A. Lagnoux. Rare Events Simulation. Publication du Laboratoire de Statistique et Probabilités, Toulouse III, 2003.
11. R. D. Reiss and M. Thomas. Statistical Analysis of Extreme Values. Birkhäuser, 1997.
12. M.N. Rosenbluth and A.W. Rosenbluth. Monte-Carlo calculations of the average extension of macromolecular chains. J. Chem. Phys., 23:356-359, 1995.
13. A. Sznitman. Brownian Motion Obstacles and Random Media. Springer-Verlag, 1998.
14. A.N. Van der Vaart and J.A. Wellner. Weak Convergence and Empirical Processes with Applications to Statistics. Series in Statistics. Springer, 1996.
15. M. Villén-Altamirano and J. Villén-Altamirano. A method for accelerating rare event simulations. In 13th Int. Teletraffic Congress,ITC 13 (Queueing, Performance and Control in ATM), pages 71-76, Copenhagen, Denmark, 1991.
16. M. Villén-Altamirano and J. Villén-Altamirano. RESTART: An efficient and general method for fast simulation of rare events. Technical Report 7, Departamento de Mætmatica Aplicada, E.U. Informática, Universidad Politécnica de Madrid, 1997.