{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T19:03:16Z","timestamp":1770490996291,"version":"3.49.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,12,26]],"date-time":"2019-12-26T00:00:00Z","timestamp":1577318400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,12,26]],"date-time":"2019-12-26T00:00:00Z","timestamp":1577318400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2020,2]]},"DOI":"10.1007\/s11424-019-8159-3","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T06:14:55Z","timestamp":1578032095000},"page":"122-136","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Several Properties of a Nonstandard Renewal Counting Process and Their Applications"],"prefix":"10.1007","volume":"33","author":[{"given":"Rong","family":"Li","sequence":"first","affiliation":[]},{"given":"Xiuchun","family":"Bi","sequence":"additional","affiliation":[]},{"given":"Shuguang","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,12,26]]},"reference":[{"key":"8159_CR1","volume-title":"Introduction to Probability Models","author":"S M Ross","year":"2010","unstructured":"Ross S M, Introduction to Probability Models, 10th ed., Academic Press, New York, 2010.","edition":"10th ed."},{"key":"8159_CR2","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/j.insmatheco.2005.01.004","volume":"36","author":"R Kaas","year":"2005","unstructured":"Kaas R and Tang Q, A large deviation result for aggregate claims with dependent claim occurrences, Insurance Math. Econom., 2005, 36: 251\u2013259.","journal-title":"Insurance Math. Econom."},{"issue":"1","key":"8159_CR3","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1239\/jap\/1077134670","volume":"41","author":"K W Ng","year":"2004","unstructured":"Ng K W, Tang Q, Yan J, et al., Precise large deviations for sums of random variables with consistently varying tails, J. Appl. Probab., 2004, 41(1): 93\u2013107.","journal-title":"J. Appl. Probab."},{"issue":"2","key":"8159_CR4","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/j.spa.2003.07.001","volume":"108","author":"Q Tang","year":"2003","unstructured":"Tang Q and Tsitsiashvili G, Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks, Stochastic Processes and Their Applications, 2003, 108(2): 299\u2013325.","journal-title":"Stochastic Processes and Their Applications"},{"key":"8159_CR5","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s10986-009-9032-1","volume":"49","author":"J Ko\u010detova","year":"2009","unstructured":"Ko\u010detova J, Leipus R, and \u0160iaulys J, A property of the renewal counting process with application to the finite-time ruin probability, Lithuanian Mathematical Journal, 2009, 49: 55\u201361.","journal-title":"Lithuanian Mathematical Journal"},{"key":"8159_CR6","doi-asserted-by":"publisher","first-page":"2248","DOI":"10.1016\/j.spl.2013.06.009","volume":"83","author":"X C Bi","year":"2013","unstructured":"Bi X C and Zhang S G, Precise large deviation of aggregate claims in a risk model with regression-type size-dependence, Statist. Probab. Lett., 2013, 83: 2248\u20132255.","journal-title":"Statist. Probab. Lett."},{"issue":"7","key":"8159_CR7","doi-asserted-by":"publisher","first-page":"3235","DOI":"10.1080\/03610926.2015.1060338","volume":"46","author":"K Fu","year":"2017","unstructured":"Fu K and Shen X, Moderate deviations for sums of dependent claims in a size-dependent renewal risk model, Communications in Statistics \u2014 Theory and Methods, 2017, 46(7): 3235\u20133243.","journal-title":"Communications in Statistics \u2014 Theory and Methods"},{"key":"8159_CR8","doi-asserted-by":"publisher","first-page":"293","DOI":"10.2307\/3215371","volume":"34","author":"C Kl\u00fcppelberg","year":"1997","unstructured":"Kl\u00fcppelberg C and Mikosch T, Large deviations of heavy-tailed random sums with applications in insurance and finance, J. Appl. Probab., 1997, 34: 293\u2013308.","journal-title":"J. Appl. Probab."},{"key":"8159_CR9","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1239\/jap\/1197908812","volume":"44","author":"S Wang","year":"2007","unstructured":"Wang S and Wang W, Precise large deviations for sums of random variables with consistently varying tails in multi-risk models, J. Appl. Probab., 2007, 44: 889\u2013900.","journal-title":"J. Appl. Probab."},{"key":"8159_CR10","doi-asserted-by":"publisher","first-page":"1206","DOI":"10.1016\/j.spl.2007.11.016","volume":"78","author":"A Baltr\u016bnas","year":"2008","unstructured":"Baltr\u016bnas A, Leipus R, and \u0161iaulys J, Precise large deviation results for the total claim amount under subexponential claim sizes, Statist. Probab. Lett., 2008, 78: 1206\u20131214.","journal-title":"Statist. Probab. Lett."},{"key":"8159_CR11","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1016\/j.spl.2016.03.002","volume":"114","author":"X Shen","year":"2016","unstructured":"Shen X, Xu M, and Mills E, Precise large deviation results for sums of sub-exponential claims in a size-dependent renewal risk model, Statistics and Probability Letters, 2016, 114: 6\u201313.","journal-title":"Statistics and Probability Letters"},{"key":"8159_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-33483-2","volume-title":"Modeling Extremal Events for Insurance and Finance","author":"P Embrechts","year":"1997","unstructured":"Embrechts P, Kl\u00fcppelberg C, and Mikosch T, Modeling Extremal Events for Insurance and Finance, Springer, New York, 1997."},{"key":"8159_CR13","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1016\/j.spl.2006.08.021","volume":"77","author":"Y Chen","year":"2007","unstructured":"Chen Y and Zhang W, Large deviations for random sums of negatively dependent random variables with consistently varying tails, Statistics and Probability Letters, 2007, 77: 530\u2013538.","journal-title":"Statistics and Probability Letters"},{"issue":"4","key":"8159_CR14","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1214\/EJP.v11-304","volume":"11","author":"Q Tang","year":"2006","unstructured":"Tang Q, Insensitivity to negative dependence of the asymptotic behavior of precise large deviations, Electronic Journal of Probability, 2006, 11(4): 107\u2013120.","journal-title":"Electronic Journal of Probability"},{"key":"8159_CR15","doi-asserted-by":"publisher","first-page":"1290","DOI":"10.1016\/j.spl.2009.02.001","volume":"79","author":"L Liu","year":"2009","unstructured":"Liu L, Precise large deviations for dependent random variables with heavy tails, Statist. Probab. Lett., 2009, 79: 1290\u20131298.","journal-title":"Statist. Probab. Lett."},{"key":"8159_CR16","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1016\/j.spl.2007.09.040","volume":"78","author":"J Lin","year":"2008","unstructured":"Lin J, The general principle for precise large deviations of heavy-tailed random sums, Statist. Probab. Lett., 2008, 78: 749\u2013758.","journal-title":"Statist. Probab. Lett."},{"key":"8159_CR17","doi-asserted-by":"publisher","first-page":"1126","DOI":"10.1239\/aap\/1293113154","volume":"42","author":"J Li","year":"2010","unstructured":"Li J, Tang Q, and Wu R, Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model, Advances Appl. Probab., 2010, 42: 1126\u20131146.","journal-title":"Advances Appl. Probab."},{"issue":"2","key":"8159_CR18","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/j.insmatheco.2012.06.010","volume":"51","author":"Y Chen","year":"2012","unstructured":"Chen Y and Yuen K C, Precise large deviations of aggregate claims in a size-dependent renewal risk model, Insurance Math. Econom., 2012, 51(2): 457\u2013461.","journal-title":"Insurance Math. Econom."},{"issue":"4","key":"8159_CR19","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/s11401-012-0723-2","volume":"33","author":"Y Yuen","year":"2012","unstructured":"Yuen Y and Yin C, Asymptotic results for tail probabilities of sums of dependent and heavy-tailed random variables, Chinese Annals of Mathematics, 2012, 33(4): 557\u2013568.","journal-title":"Chinese Annals of Mathematics"},{"issue":"10","key":"8159_CR20","doi-asserted-by":"publisher","first-page":"2801","DOI":"10.1080\/03610926.2014.887111","volume":"45","author":"Y Yang","year":"2016","unstructured":"Yang Y and Sha L, Precise large deviations for aggregate claims, Communications in Statistics \u2014 Theory and Methods, 2016, 45(10): 2801\u20132809.","journal-title":"Communications in Statistics \u2014 Theory and Methods"},{"issue":"3","key":"8159_CR21","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.1080\/03610926.2015.1010011","volume":"46","author":"H Guo","year":"2017","unstructured":"Guo H, Wang S, and Zhang C, Precise large deviations of aggregate claims in a compound size-dependent renewal risk model, Comm. Statist. Theory Methods, 2017, 46(3): 1107\u20131116.","journal-title":"Comm. Statist. Theory Methods"},{"issue":"2","key":"8159_CR22","doi-asserted-by":"publisher","first-page":"736","DOI":"10.1080\/03610926.2015.1004094","volume":"46","author":"Z Hua","year":"2017","unstructured":"Hua Z, Song L, Lu D, et al., Precise large deviations for the difference of two sums of END random variables with heavy tails, Comm. Statist. Theory Methods, 2017, 46(2): 736\u2013746.","journal-title":"Comm. Statist. Theory Methods"},{"issue":"5","key":"8159_CR23","doi-asserted-by":"publisher","first-page":"2354","DOI":"10.1080\/03610926.2015.1044666","volume":"46","author":"X Liu","year":"2017","unstructured":"Liu X, Yu C, and Gao Q, Precise large deviations of aggregate claim amount in a dependent renewal risk model, Comm. Statist. Theory Methods, 2017, 46(5): 2354\u20132363.","journal-title":"Comm. Statist. Theory Methods"},{"key":"8159_CR24","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1016\/j.spl.2011.08.024","volume":"82","author":"X M Shen","year":"2012","unstructured":"Shen X M and Zhang Y, Moderate deviations for a risk model based on the customer-arrival process, Statist. Probab. Lett., 2012, 82: 116\u2013122.","journal-title":"Statist. Probab. Lett."},{"key":"8159_CR25","doi-asserted-by":"publisher","first-page":"1527","DOI":"10.1007\/s10114-007-0941-9","volume":"23","author":"F Q Gao","year":"2007","unstructured":"Gao F Q, Moderate deviations for random sums of heavy-tailed random variables, Acta Math. Sin., 2007, 23: 1527\u20131536.","journal-title":"Acta Math. Sin."},{"key":"8159_CR26","doi-asserted-by":"publisher","first-page":"1421","DOI":"10.1007\/s11425-010-4012-9","volume":"53","author":"L Liu","year":"2010","unstructured":"Liu L, Necessary and sufficient condtitions for moderate deviations of dependent random variables with heavy tails, Science China: Mathematics, 2010, 53: 1421\u20131434.","journal-title":"Science China: Mathematics"},{"issue":"7","key":"8159_CR27","doi-asserted-by":"publisher","first-page":"3235","DOI":"10.1080\/03610926.2015.1060338","volume":"46","author":"K A Fu","year":"2017","unstructured":"Fu K A and Shen X M, Moderate deviations for sums of dependent claims in a size-dependent renewal risk model, Communications in Statistics \u2014 Theory and Methods, 2017, 46(7): 3235\u20133243.","journal-title":"Communications in Statistics \u2014 Theory and Methods"},{"key":"8159_CR28","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511721434","volume-title":"Regular Variation","author":"N H Bingham","year":"1987","unstructured":"Bingham N H, Goldie C M, and Teugels J L, Regular Variation, Cambridge University Press, Cambridge, 1987."},{"key":"8159_CR29","doi-asserted-by":"publisher","first-page":"665","DOI":"10.2748\/tmj\/1325886286","volume":"63","author":"Y T Liu","year":"2011","unstructured":"Liu Y T, Ma Z M, and Zhou C, Web Markov skeleton processes and their applications, Tohoku Mathematical Journal, 2011, 63: 665\u2013695.","journal-title":"Tohoku Mathematical Journal"},{"key":"8159_CR30","doi-asserted-by":"crossref","unstructured":"Ma Z M, Liu Y T, and Zhou C, Further study on web Markov skeleton processes, Stochastic Analysis and Application to Finance, 2012, 313\u2013339.","DOI":"10.1142\/9789814383585_0016"},{"issue":"3","key":"8159_CR31","first-page":"143","volume":"43","author":"V M Korchevsky","year":"2010","unstructured":"Korchevsky V M and Petrov V V, On the strong law of large numbers for sequences of dependent random variables, Vestnik St. Petersburg University, Mathematics, 2010, 43(3): 143\u2013147.","journal-title":"Mathematics"},{"key":"8159_CR32","first-page":"1","volume":"260","author":"R Li","year":"2018","unstructured":"Li R, Bi X C, and Zhang S G, Web renewal counting processes and their applications in insurance, Journal of Inequalities and Applications, 2018, 260: 1\u201315.","journal-title":"Journal of Inequalities and Applications"}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-019-8159-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-019-8159-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-019-8159-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T00:16:17Z","timestamp":1608855377000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-019-8159-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,26]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,2]]}},"alternative-id":["8159"],"URL":"https:\/\/doi.org\/10.1007\/s11424-019-8159-3","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,26]]},"assertion":[{"value":"23 May 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 December 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}