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In this article we study dynamic importance sampling schemes for sums of independent and identically distributed random variables with regularly varying tails. The number of summands can be random but must be independent of the summands. For estimating the probability that the sum exceeds a given threshold, we explicitly identify a class of dynamic importance sampling algorithms with bounded relative errors. In fact, these schemes are nearly asymptotically optimal in the sense that the second moment of the corresponding importance sampling estimator can be made as close as desired to the minimal possible value.<\/jats:p>","DOI":"10.1145\/1243991.1243995","type":"journal-article","created":{"date-parts":[[2007,9,14]],"date-time":"2007-09-14T13:44:55Z","timestamp":1189777495000},"page":"14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":38,"title":["Importance sampling for sums of random variables with regularly varying tails"],"prefix":"10.1145","volume":"17","author":[{"given":"Paul","family":"Dupuis","sequence":"first","affiliation":[{"name":"Brown University, Providence, RI"}]},{"given":"Kevin","family":"Leder","sequence":"additional","affiliation":[{"name":"Brown University, Providence, RI"}]},{"given":"Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"Brown University, Providence, RI"}]}],"member":"320","published-online":{"date-parts":[[2007,7]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"Asmussen S. 2000. Ruin Probabilities. World Scientific Singapore.  Asmussen S. 2000. Ruin Probabilities. World Scientific Singapore.","DOI":"10.1142\/2779"},{"key":"e_1_2_1_2_1","unstructured":"Asmussen S. and Kroese D. 2004. Improved algorithms for rare event simulation with heavy tails. Tech. rep. The Danish National Research Foundation: Network in Mathematical Physics and Stochastics.  Asmussen S. and Kroese D. 2004. Improved algorithms for rare event simulation with heavy tails. Tech. rep. The Danish National Research Foundation: Network in Mathematical Physics and Stochastics."},{"volume-title":"Proceedings of the 2005 Winter Simulation Conference, F. Armstrong, J. Joines, M. Kuhl, and N. Steiger, Eds.","author":"Bassamboo A.","key":"e_1_2_1_3_1"},{"key":"e_1_2_1_4_1","unstructured":"Billingsley P. 1968. Convergence of Probability Measures. John Wiley New York.  Billingsley P. 1968. Convergence of Probability Measures. John Wiley New York."},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","unstructured":"Bingham N. Goldie C. and Teugels J. 1987. Regular Variation. Cambridge University Press Cambridge.  Bingham N. Goldie C. and Teugels J. 1987. Regular Variation. Cambridge University Press Cambridge.","DOI":"10.1017\/CBO9780511721434"},{"key":"e_1_2_1_6_1","unstructured":"Crovella M. Taqqu M. and Bestavros A. 1998. Heavy-tailed probability distributions in the World Wide Web. In A Practical Guide to Heavy Tails R. Adler R. Feldman and M. Taqqu Eds. Birkhauser Boston 3--26.   Crovella M. Taqqu M. and Bestavros A. 1998. Heavy-tailed probability distributions in the World Wide Web. In A Practical Guide to Heavy Tails R. Adler R. Feldman and M. Taqqu Eds. Birkhauser Boston 3--26."},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","unstructured":"Dupuis P. and Ellis. R. S. 1997. A Weak Convergence Approach to the Theory of Large Deviations. John Wiley & Sons New York.  Dupuis P. and Ellis. R. S. 1997. A Weak Convergence Approach to the Theory of Large Deviations. John Wiley & Sons New York.","DOI":"10.1002\/9781118165904"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1080\/10451120410001733845"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/105051604000001016"},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","unstructured":"Embrechts P. Kluppelberg C. and Mikosch T. 1997. Modelling Extremal Events. Springer Berlin.   Embrechts P. Kluppelberg C. and Mikosch T. 1997. Modelling Extremal Events. 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