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Model. Comput. Simul."],"published-print":{"date-parts":[[2013,10]]},"abstract":"<jats:p>In this article, rare-event simulation for stochastic recurrence equations of the form<\/jats:p>\n          <jats:p>\n            <jats:italic>X<\/jats:italic>\n            <jats:sub>\n              <jats:italic>n<\/jats:italic>\n              +1\n            <\/jats:sub>\n            =\n            <jats:italic>A<\/jats:italic>\n            <jats:sub>\n              <jats:italic>n<\/jats:italic>\n              +1\n            <\/jats:sub>\n            <jats:italic>X<\/jats:italic>\n            <jats:sub>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sub>\n            +\n            <jats:italic>B<\/jats:italic>\n            <jats:sub>\n              <jats:italic>n<\/jats:italic>\n              +1\n            <\/jats:sub>\n            ,\n            <jats:italic>X<\/jats:italic>\n            <jats:sub>0<\/jats:sub>\n            =0\n          <\/jats:p>\n          <jats:p>\n            is studied, where {\n            <jats:italic>A<\/jats:italic>\n            <jats:sub>n<\/jats:sub>\n            ;\n            <jats:italic>n<\/jats:italic>\n            \u2265 1} and {\n            <jats:italic>B<\/jats:italic>\n            <jats:sub>n<\/jats:sub>\n            ;\n            <jats:italic>n<\/jats:italic>\n            \u2265 1} are independent sequences consisting of independent and identically distributed real-valued random variables. It is assumed that the tail of the distribution of\n            <jats:italic>B<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            is regularly varying, whereas the distribution of\n            <jats:italic>A<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            has a suitably light tail. The problem of efficient estimation, via simulation, of quantities such as\n            <jats:italic>P<\/jats:italic>\n            {\n            <jats:italic>X<\/jats:italic>\n            <jats:sub>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sub>\n            &gt;b} and\n            <jats:italic>P<\/jats:italic>\n            {sup\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n              \u2264\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sub>\n            <jats:italic>X<\/jats:italic>\n            <jats:sub>k<\/jats:sub>\n            &gt; b} for large\n            <jats:italic>b<\/jats:italic>\n            and\n            <jats:italic>n<\/jats:italic>\n            is studied. Importance sampling strategies are investigated that provide unbiased estimators with bounded relative error as\n            <jats:italic>b<\/jats:italic>\n            and\n            <jats:italic>n<\/jats:italic>\n            tend to infinity.\n          <\/jats:p>","DOI":"10.1145\/2517451","type":"journal-article","created":{"date-parts":[[2013,12,17]],"date-time":"2013-12-17T13:36:15Z","timestamp":1387287375000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Rare-event simulation for stochastic recurrence equations with heavy-tailed innovations"],"prefix":"10.1145","volume":"23","author":[{"given":"Jose","family":"Blanchet","sequence":"first","affiliation":[{"name":"Columbia University"}]},{"given":"Henrik","family":"Hult","sequence":"additional","affiliation":[{"name":"Royal Institute of Technology"}]},{"given":"Kevin","family":"Leder","sequence":"additional","affiliation":[{"name":"University of Minnesota"}]}],"member":"320","published-online":{"date-parts":[[2013,12,16]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1214\/11-AAP792"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.2143\/AST.27.2.542054"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/3318578"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0001867800001099"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(01)00156-9"},{"key":"e_1_2_2_6_1","doi-asserted-by":"crossref","unstructured":"Bingham N. H. Goldie C. M. and Teugels I. L. 1987. Regular Variation. Cambridge University Press Cambridge United Kingdom.  Bingham N. H. Goldie C. M. and Teugels I. L. 1987. Regular Variation. Cambridge University Press Cambridge United Kingdom.","DOI":"10.1017\/CBO9780511721434"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1214\/07-AAP485"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/2331140.2331141"},{"key":"e_1_2_2_9_1","first-page":"3824","article-title":"State-dependent importance sampling for rare-event simulation: An overview and recent advances","volume":"17","author":"Blanchet J.","year":"2011","unstructured":"Blanchet , J. and Lam , H. 2011 . State-dependent importance sampling for rare-event simulation: An overview and recent advances . Surv. Oper. Res. Manage. Sci. 17 , 3824 -- 3831 . Blanchet, J. and Lam, H. 2011. State-dependent importance sampling for rare-event simulation: An overview and recent advances. Surv. Oper. Res. Manage. Sci. 17, 3824--3831.","journal-title":"Surv. Oper. Res. Manage. Sci."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1308662639"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1276784893"},{"key":"e_1_2_2_12_1","unstructured":"Blanchet J. Liu J. C. and Glynn P. 2011. Efficient rare event simulation for regularly varying multi-server queues. Submitted (2011).  Blanchet J. Liu J. C. and Glynn P. 2011. Efficient rare event simulation for regularly varying multi-server queues. Submitted (2011)."},{"volume-title":"Proceedings of the Winter Simulation Conference. 468--476","author":"Boots N.","key":"e_1_2_2_13_1","unstructured":"Boots , N. and Shahabuddin , P . 2001. Statistical tools for simulation design and analysis: Simulating ruin probabilities in insurance risk processes with subexponential claims . In Proceedings of the Winter Simulation Conference. 468--476 . Boots, N. and Shahabuddin, P. 2001. Statistical tools for simulation design and analysis: Simulating ruin probabilities in insurance risk processes with subexponential claims. 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