Effective branching splitting method under cost constraint

Stochastic Processes and their Applications

Volumn 118, Issue 10, 2008, Pages 1820-1851

  Lagnoux Renaudie, Agnès ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Branching processes; Cost function; Galton Watson; Iterated functions; Laplace transform; Rare event; Simulation; Splitting method

Indexed keywords

BRANCHING PROCESSES; COST FUNCTION; GALTON-WATSON; ITERATED FUNCTIONS; LAPLACE TRANSFORM; RARE EVENT; SIMULATION; SPLITTING METHOD;

ERROR ANALYSIS;

EID: 50649107077     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2007.10.009     Document Type: Article

References (31)

1. Aldous D. Probability Approximations via the Poisson Clumping Heuristic. Applied Mathematical Sciences vol. 77 (1989), Springer-Verlag
2. Aldous D., and Vazirani U.V. 'Go with the winners' algorithms. IEEE Symposium on Foundations of Computer Science 7 (1994) 492-501
3. Athreya K.B., and Karlin S. On branching processes with random environments. I. Extinction probabilities. Ann. Math. Statist. 42 (1971) 1499-1520
4. Athreya K.B., and Karlin S. Branching processes with random environments. II. Limit theorems. Ann. Math. Statist. 42 (1971) 1843-1858
5. Athreya K.B., and Ney P.E. Branching Processes, in: Die Grundlehren der mathematischen Wissenschaften, Band 196 (1972), Springer-Verlag
6. n in the critical case. Ann. Probab. 25 1 (1997) 478-493
7. P.T. de Boer, Analysis and efficient simulation of queueing models of telecommunication systems, Ph.D. Thesis, University of Twente, The Netherlands, 2000
8. Bougerol P., and Picard N. Strict stationarity of generalized autoregressive processes. Ann. Probab. 20 4 (1992) 1714-1730
9. n with stationary coefficients. Adv. in Appl. Probab. 18 1 (1986) 211-220
10. F. Cérou, A. Guyader, Adaptive multilevel splitting for rare event analysis, Rapport de recherche de l'INRIA - Rennes, Equipe: ASPI, 2005
11. Del Moral P. Feynman-Kac formulae, Genealogical and interacting particle systems with applications, Probability and its Applications (New York) (2004), Springer-Verlag, New York
12. Diaconis P., and Freedman D. Iterated random functions. SIAM Rev. 41 1 (1999) 45-76
13. Diaconis P., and Holmes S. Three examples of Monte-Carlo Markov chains: at the interface between statistical computing, computer science, and statistical mechanics, Discrete probability and algorithms (Minneapolis, MN, 1993). IMA Vol. Math. Appl. 72 (1995) 43-56
14. Doucet A., de Freitas N., and Gordon N. An introduction to sequential Monte Carlo methods, Sequential Monte Carlo methods in practice. Stat. Eng. Inf. Sci. (2001), Springer 3-14
15. M.J.J. Garvels, The splitting method in rare event simulation, Ph.D. Thesis, University of Twente, The Netherlands, 2000
16. Glasserman P., Heidelberger P., Shahabuddin P., and Zaji T. A large deviations perspective on the efficiency of multilevel splitting. IEEE Trans. Automat. Control 43 12 (1998) 1666-1679
17. Glasserman P., Heidelberger P., Shahabuddin P., and Zajic T. Multilevel splitting for estimating rare event probabilities. Oper. Res. 47 4 (1999) 585-600
18. Guivarc'h Y., Le Page E., and Liu Q. Normalisation d'un processus de branchement critique dans un environnement aléatoire. C. R. Math. Acad. Sci. Paris 337 9 (2003) 603-608
19. T.E. Harris, The theory of branching processes, Dover Phoenix Editions, 2002, Corrected reprint of the 1963 original [Springer, Berlin; MR29 #664]
20. Heidelberger P. Fast Simulation of Rare Events in Queueing and Reliability Models. ACM Trans. Model. Simul. 5 1 (1995) 43-85
21. Jerrum M., and Sinclair A. The Markov chain Monte Carlo method: an approach to approximate counting and integration. Approximation Algorithms for NP-hard Problems (1997) 482-520
22. Kesten H. Random difference equations and renewal theory for products of random matrices. Acta Math. Acad. Sci. Hungar. 131 (1973) 207-248
23. Lagnoux A. Rare event simulation. Probab. Engrg. Inform. Sci. 20 (2006) 45-66
24. R. Lyons, Probability on trees and networks. http://mypage.iu.edu/rdlyons/ 2002
25. Maksimov V.M. A generalized Bernoulli scheme and its limit distributions. Teor. Verojatnost. i Primenen. 18 (1973) 547-556
26. Sadowsky J.S. On Monte Carlo estimation of large deviations probabilities. Ann. Appl. Probab. 6 2 (1996) 399-422
27. Smith W.L., and Wilkinson W.E. On branching processes in random environments. Ann. Math. Statist. 40 (1969) 814-827
28. Tanny D. Limit theorems for branching processes in a random environment. Ann. Probab. 5 1 (1977) 100-116
29. Vervaat W. On a stochastic difference equation and a representation of nonnegative infinitely divisible random variables. Adv. in Appl. Probab. 11 4 (1979) 750-783
30. M. Villén-Altamirano, J. Villén-Altamirano, RESTART: A method for accelerating rare event simulations, in: 13th International Teletraffic Congress, Copenhagen, (1991) 71-76
31. Villén-Altamirano Manuel, Villén-Altamirano José, Restart: An efficient and general method for fast simulation of Rare Event, Tech. Rept. No. 7, Departamento de Mathematica Aplicada, E.U. Informática, Universidad Polytéchnica de Madrid, 1997