{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T20:52:11Z","timestamp":1680468731485},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3-4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2011,8]]},"DOI":"10.1007\/s11134-011-9242-1","type":"journal-article","created":{"date-parts":[[2011,7,8]],"date-time":"2011-07-08T21:24:15Z","timestamp":1310160255000},"page":"275-284","source":"Crossref","is-referenced-by-count":4,"title":["Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations"],"prefix":"10.1007","volume":"68","author":[{"given":"Rafa\u0142","family":"Kulik","sequence":"first","affiliation":[]},{"given":"Zbigniew","family":"Palmowski","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,7,9]]},"reference":[{"issue":"2","key":"9242_CR1","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF03191909","volume":"103","author":"H. Albrecher","year":"2009","unstructured":"Albrecher, H., Thonhauser, S.: Optimality results for dividend problems in insurance. RACSAM Rev. R. Acad. Cien. Ser. A. Mat. 103(2), 295\u2013320 (2009)","journal-title":"RACSAM Rev. R. Acad. Cien. Ser. A. Mat."},{"key":"9242_CR2","unstructured":"Antunes, N., Fricker, C., Guillemin, F., Robert, P.: Perturbation analysis of the area swept under the queue length process of a variable M\/M\/1 queue. Performance (2005)"},{"key":"9242_CR3","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1214\/105051606000000709","volume":"17","author":"F. Avram","year":"2007","unstructured":"Avram, F., Palmowski, Z., Pistorius, M.: On the optimal dividend problem for a spectrally negative L\u00e9vy process. Ann. Appl. Probab. 17, 156\u2013180 (2007)","journal-title":"Ann. Appl. Probab."},{"issue":"6","key":"9242_CR4","doi-asserted-by":"crossref","first-page":"2421","DOI":"10.1214\/08-AAP529","volume":"18","author":"F. Avram","year":"2008","unstructured":"Avram, F., Palmowski, Z., Pistorius, M.: Exit problem of a two-dimensional risk process from a cone: exact and asymptotic results. Ann. Appl. Probab. 18(6), 2421\u20132449 (2008)","journal-title":"Ann. Appl. Probab."},{"key":"9242_CR5","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.spa.2004.01.005","volume":"111","author":"A. Baltrunas","year":"2004","unstructured":"Baltrunas, A., Daley, D.J., Kl\u00fcppelberg, C.: Tail behaviour of the busy period of a GI\/GI\/1 queue with subexponential service times. Stoch. Process. Appl. 111, 237\u2013258 (2004)","journal-title":"Stoch. Process. Appl."},{"issue":"1","key":"9242_CR6","doi-asserted-by":"crossref","first-page":"33","DOI":"10.5802\/afst.1016","volume":"11","author":"J. Bertoin","year":"2002","unstructured":"Bertoin, J., Yor, M.: On the entire moments of self-similar Markov processes and exponential functionals of L\u00e9vy processes. Ann. Fac. Sci. Toulouse Math. (6) 11(1), 33\u201345 (2002)","journal-title":"Ann. Fac. Sci. Toulouse Math. (6)"},{"key":"9242_CR7","series-title":"Progr. Probab.","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/978-3-0348-7943-9_3","volume-title":"Seminar on Stochastic Analysis, Random Fields and Applications IV","author":"J. Bertoin","year":"2004","unstructured":"Bertoin, J., Biane, P., Yor, M.: Poissonian exponential functionals, q-series, q-integrals, and the moment problem for log-normal distributions. In: Seminar on Stochastic Analysis, Random Fields and Applications IV. Progr. Probab., vol.\u00a058, pp. 45\u201356. Birkh\u00e4user, Basel (2004)"},{"issue":"2","key":"9242_CR8","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.jmaa.2010.01.051","volume":"367","author":"R. Biard","year":"2010","unstructured":"Biard, R., Loisel, S., Maccib, C., Veraverbeke, N.: Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation. J. Math. Anal. Appl. 367(2), 535\u2013549 (2010)","journal-title":"J. Math. Anal. Appl."},{"key":"9242_CR9","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1239\/jap\/1044476835","volume":"40","author":"A.A. Borovkov","year":"2003","unstructured":"Borovkov, A.A., Boxma, O.J., Palmowski, Z.: On the integral of the workload process of the single server queue. J. Appl. Probab. 40, 200\u2013225 (2003)","journal-title":"J. Appl. Probab."},{"key":"9242_CR10","series-title":"Bibl. Rev. Mat. Iberoamericana","first-page":"73","volume-title":"Exponential Functionals and Principal Values Related to Brownian Motion","author":"P. Carmona","year":"1997","unstructured":"Carmona, P., Petit, F., Yor, M.: On the distribution and asymptotic results for exponential functionals of L\u00e9vy processes. In: Exponential Functionals and Principal Values Related to Brownian Motion. Bibl. Rev. Mat. Iberoamericana, pp. 73\u2013130 (1997)"},{"issue":"12","key":"9242_CR11","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1016\/j.peva.2010.06.002","volume":"67","author":"K.R. Duffy","year":"2010","unstructured":"Duffy, K.R., Meyn, S.P.: Most likely paths to error when estimating the mean of a reflected random walk. Perform. Eval. 67(12), 1290\u20131303 (2010)","journal-title":"Perform. Eval."},{"issue":"1","key":"9242_CR12","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1214\/aoap\/1177005985","volume":"1","author":"C.M. Goldie","year":"1991","unstructured":"Goldie, C.M.: Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1(1), 126\u2013166 (1991)","journal-title":"Ann. Appl. Probab."},{"key":"9242_CR13","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1023\/A:1019100617896","volume":"29","author":"F. Guillemin","year":"1998","unstructured":"Guillemin, F., Pinchon, D.: On the area swept under the occupation process of an M\/M\/1 queue in a busy period. Queueing Syst. 29, 383\u2013398 (1998)","journal-title":"Queueing Syst."},{"key":"9242_CR14","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1214\/009117906000000548","volume":"35","author":"H. Hult","year":"2007","unstructured":"Hult, H., Linskog, F.: Extremal behavior of stochastic integrals driven by regularly varying L\u00e9vy processes. Ann. Probab. 35, 309\u2013339 (2007)","journal-title":"Ann. Probab."},{"key":"9242_CR15","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1287\/moor.1030.0082","volume":"29","author":"P.R. Jelenkovi\u0107","year":"2004","unstructured":"Jelenkovi\u0107, P.R., Mom\u010dilovi\u0107, P.: Large deviations of square root insensitive random sums. Math. Oper. Res. 29, 398\u2013406 (2004)","journal-title":"Math. Oper. Res."},{"key":"9242_CR16","doi-asserted-by":"crossref","first-page":"8421","DOI":"10.1088\/0305-4470\/37\/35\/002","volume":"37","author":"M.J. Kearney","year":"2004","unstructured":"Kearney, M.J.: On a random area variable arising in discrete-time queues and compact directed percolation. J. Phys. A, Math. Gen. 37, 8421\u20138431 (2004)","journal-title":"J. Phys. A, Math. Gen."},{"key":"9242_CR17","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF02392040","volume":"131","author":"H. Kesten","year":"1973","unstructured":"Kesten, H.: Random difference equations and renewal theory for products of random matrices. Acta Math. 131, 207\u2013248 (1973)","journal-title":"Acta Math."},{"key":"9242_CR18","doi-asserted-by":"crossref","first-page":"494","DOI":"10.2307\/3212173","volume":"8","author":"E.K. Kyprianou","year":"1971","unstructured":"Kyprianou, E.K.: On the quasi-stationary distribution of the virtual waiting time in queues with Poisson arrivals. J. Appl. Probab. 8, 494\u2013507 (1971)","journal-title":"J. Appl. Probab."},{"key":"9242_CR19","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1214\/08-AIHP307","volume":"46","author":"A. Kyprianou","year":"2010","unstructured":"Kyprianou, A., Loeffen, R.: Refracted L\u00e9vy processes. Ann. Inst. H. Poincar\u00e9 Probab. Stat. 46, 24\u201344 (2010)","journal-title":"Ann. Inst. H. Poincar\u00e9 Probab. Stat."},{"issue":"2","key":"9242_CR20","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1239\/jap\/1183667412","volume":"44","author":"A. Kyprianou","year":"2007","unstructured":"Kyprianou, A., Palmowski, Z.: Distributional study of De Finetti\u2019s dividend problem for a general L\u00e9vy insurance risk process. J. Appl. Probab. 44(2), 428\u2013443 (2007)","journal-title":"J. Appl. Probab."},{"key":"9242_CR21","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s11134-005-0926-2","volume":"50","author":"R. Kulik","year":"2005","unstructured":"Kulik, R., Palmowski, Z.: Tail behaviour of the area under queue length process of a single server queue with regularly varying service times. Queueing Syst. 50, 299\u2013323 (2005)","journal-title":"Queueing Syst."},{"key":"9242_CR22","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s11134-008-9094-5","volume":"60","author":"P. Lieshout","year":"2008","unstructured":"Lieshout, P., Mandjes, M.: Asymptotic analysis of Levy-driven tandem queues. Queueing Syst. 60, 203\u2013226 (2008)","journal-title":"Queueing Syst."},{"key":"9242_CR23","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s00186-007-0149-x","volume":"66","author":"P. Lieshout","year":"2007","unstructured":"Lieshout, P., Mandjes, M.: Brownian tandem queues. Math. Methods Oper. Res. 66, 275\u2013298 (2007)","journal-title":"Math. Methods Oper. Res."},{"key":"9242_CR24","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.spa.2005.09.002","volume":"116","author":"K. Maulik","year":"2006","unstructured":"Maulik, K., Zwart, B.: Tail asymptotics for exponential functionals of L\u00e9vy processes. Stoch. Process. Appl. 116, 156\u2013177 (2006)","journal-title":"Stoch. Process. Appl."},{"issue":"1","key":"9242_CR25","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1214\/105051605000000737","volume":"16","author":"S.P. Meyn","year":"2006","unstructured":"Meyn, S.P.: Large deviation asymptotics and control variates for simulating large functions. Ann. Appl. Probab. 16(1), 310\u2013339 (2006)","journal-title":"Ann. Appl. Probab."},{"key":"9242_CR26","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804410","volume-title":"Control Techniques for Complex Networks","author":"S.P. Meyn","year":"2007","unstructured":"Meyn, S.P.: Control Techniques for Complex Networks. Cambridge University Press, Cambridge (2007)"},{"key":"9242_CR27","volume-title":"Stochastic Control in Insurance","author":"H. Schmidli","year":"2008","unstructured":"Schmidli, H.: Stochastic Control in Insurance. Springer, New York (2008)"},{"key":"9242_CR28","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1287\/moor.26.3.485.10584","volume":"26","author":"A.P. Zwart","year":"2001","unstructured":"Zwart, A.P.: Tail asymptotics for the busy period in the GI\/G\/1 queue. Math. Oper. Res. 26, 485\u2013493 (2001)","journal-title":"Math. Oper. Res."}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.springerlink.com\/index\/pdf\/10.1007\/s11134-011-9242-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,20]],"date-time":"2017-06-20T03:00:04Z","timestamp":1497927604000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-011-9242-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,9]]},"references-count":28,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2011,8]]}},"alternative-id":["9242"],"URL":"https:\/\/doi.org\/10.1007\/s11134-011-9242-1","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7,9]]}}}