{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:24:18Z","timestamp":1773145458864,"version":"3.50.1"},"reference-count":33,"publisher":"Institute of Mathematical Statistics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Inst. H. Poincar\u00e9 Probab. Statist."],"published-print":{"date-parts":[[2017,8,1]]},"DOI":"10.1214\/16-aihp757","type":"journal-article","created":{"date-parts":[[2017,7,21]],"date-time":"2017-07-21T08:00:58Z","timestamp":1500624058000},"source":"Crossref","is-referenced-by-count":17,"title":["Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems"],"prefix":"10.1214","volume":"53","author":[{"given":"Ana Cristina Moreira","family":"Freitas","sequence":"first","affiliation":[]},{"given":"Jorge Milhazes","family":"Freitas","sequence":"additional","affiliation":[]},{"given":"Sandro","family":"Vaienti","sequence":"additional","affiliation":[]}],"member":"108","reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"[1] R. Aimino, H. Hu, M. Nicol, A. T\u00f6r\u00f6k and S. Vaienti. Polynomial loss of memory for maps of the interval with a neutral fixed point. <i>Discrete Contin. Dyn. Syst.<\/i> <b>35<\/b> (3) (2015) 793\u2013806. <a href=\"doi:10.3934\/dcds.2015.35.793\">doi:10.3934\/dcds.2015.35.793<\/a>.","DOI":"10.3934\/dcds.2015.35.793"},{"key":"2","doi-asserted-by":"crossref","unstructured":"[2] J. F. Alves, J. M. Freitas, S. Luzzatto and S. Vaienti. From rates of mixing to recurrence times via large deviations. <i>Adv. Math.<\/i> <b>228<\/b> (2) (2011) 1203\u20131236. Available at <a href=\"arXiv:1007.3771\">arXiv:1007.3771<\/a>. <a href=\"doi:10.1016\/j.aim.2011.06.014\">doi:10.1016\/j.aim.2011.06.014<\/a>.","DOI":"10.1016\/j.aim.2011.06.014"},{"key":"3","doi-asserted-by":"crossref","unstructured":"[3] L. Arnold. <i>Random Dynamical Systems. Springer Monographs in Mathematics<\/i>. Springer-Verlag, Berlin, 1998. <a href=\"doi:10.1007\/978-3-662-12878-7\">doi:10.1007\/978-3-662-12878-7<\/a>.","DOI":"10.1007\/978-3-662-12878-7"},{"key":"4","doi-asserted-by":"crossref","unstructured":"[4] H. Ayta\u00e7, J. M. Freitas and S. Vaienti. Laws of rare events for deterministic and random dynamical systems. <i>Trans. Amer. Math. Soc.<\/i> <b>367<\/b> (11) (2015) 8229\u20138278. <a href=\"doi:10.1090\/S0002-9947-2014-06300-9\">doi:10.1090\/S0002-9947-2014-06300-9<\/a>.","DOI":"10.1090\/S0002-9947-2014-06300-9"},{"key":"5","doi-asserted-by":"crossref","unstructured":"[5] W. Bahsoun and S. Vaienti. Escape rates formulae and metastability for randomly perturbed maps. <i>Nonlinearity<\/i> <b>26<\/b> (5) (2013) 1415\u20131438. <a href=\"doi:10.1088\/0951-7715\/26\/5\/1415\">doi:10.1088\/0951-7715\/26\/5\/1415<\/a>.","DOI":"10.1088\/0951-7715\/26\/5\/1415"},{"key":"6","doi-asserted-by":"crossref","unstructured":"[6] D. Berend and V. Bergelson. Ergodic and mixing sequences of transformations. <i>Ergodic Theory Dynam. Systems<\/i> <b>4<\/b> (3) (1984) 353\u2013366. <a href=\"doi:10.1017\/S0143385700002509\">doi:10.1017\/S0143385700002509<\/a>.","DOI":"10.1017\/S0143385700002509"},{"key":"7","doi-asserted-by":"crossref","unstructured":"[7] M. R. Chernick, T. Hsing and W. P. McCormick. Calculating the extremal index for a class of stationary sequences. <i>Adv. in Appl. Probab.<\/i> <b>23<\/b> (4) (1991) 835\u2013850. <a href=\"doi:10.2307\/1427679\">doi:10.2307\/1427679<\/a>.","DOI":"10.1017\/S0001867800023971"},{"key":"8","doi-asserted-by":"crossref","unstructured":"[8] P. Collet. Statistics of closest return for some non-uniformly hyperbolic systems. <i>Ergodic Theory Dynam. Systems<\/i> <b>21<\/b> (2) (2001) 401\u2013420. <a href=\"doi:10.1017\/S0143385701001201\">doi:10.1017\/S0143385701001201<\/a>.","DOI":"10.1017\/S0143385701001201"},{"key":"9","doi-asserted-by":"crossref","unstructured":"[9] J.-P. Conze and A. Raugi. Limit theorems for sequential expanding dynamical systems on $[0,1]$. In <i>Ergodic Theory and Related Fields<\/i> 89\u2013121. <i>Contemp. Math.<\/i> <b>430<\/b>. Amer. Math. Soc., Providence, RI, 2007. <a href=\"doi:10.1090\/conm\/430\/08253\">doi:10.1090\/conm\/430\/08253<\/a>.","DOI":"10.1090\/conm\/430\/08253"},{"key":"10","doi-asserted-by":"crossref","unstructured":"[10] M. Falk, J. H\u00fcsler and R.-D. Reiss. <i>Laws of Small Numbers: Extremes and Rare Events<\/i>, extended edition. Birkh\u00e4user\/Springer Basel AG, Basel, 2011. <a href=\"doi:10.1007\/978-3-0348-0009-9\">doi:10.1007\/978-3-0348-0009-9<\/a>.","DOI":"10.1007\/978-3-0348-0009-9"},{"key":"11","doi-asserted-by":"crossref","unstructured":"[11] A. C. M. Freitas and J. M. Freitas. On the link between dependence and independence in extreme value theory for dynamical systems. <i>Statist. Probab. Lett.<\/i> <b>78<\/b> (9) (2008) 1088\u20131093. <a href=\"doi:10.1016\/j.spl.2007.11.002\">doi:10.1016\/j.spl.2007.11.002<\/a>.","DOI":"10.1016\/j.spl.2007.11.002"},{"key":"12","doi-asserted-by":"crossref","unstructured":"[12] A. C. M. Freitas, J. M. Freitas and M. Todd. Hitting time statistics and extreme value theory. <i>Probab. Theory Related Fields<\/i> <b>147<\/b> (3\u20134) (2010) 675\u2013710. Available at <a href=\"arXiv:0804.2887\">arXiv:0804.2887<\/a>. <a href=\"doi:10.1007\/s00440-009-0221-y\">doi:10.1007\/s00440-009-0221-y<\/a>.","DOI":"10.1007\/s00440-009-0221-y"},{"key":"13","doi-asserted-by":"crossref","unstructured":"[13] A. C. M. Freitas, J. M. Freitas and M. Todd. Extreme value laws in dynamical systems for non-smooth observations. <i>J. Stat. Phys.<\/i> <b>142<\/b> (1) (2011) 108\u2013126. Available at <a href=\"arXiv:1006.3276\">arXiv:1006.3276<\/a>. <a href=\"doi:10.1007\/s10955-010-0096-4\">doi:10.1007\/s10955-010-0096-4<\/a>.","DOI":"10.1007\/s10955-010-0096-4"},{"key":"14","doi-asserted-by":"crossref","unstructured":"[14] A. C. M. Freitas, J. M. Freitas and M. Todd. The extremal index, hitting time statistics and periodicity. <i>Adv. Math.<\/i> <b>231<\/b> (5) (2012) 2626\u20132665. Available at <a href=\"arXiv:1008.1350\">arXiv:1008.1350<\/a>. <a href=\"doi:10.1016\/j.aim.2012.07.029\">doi:10.1016\/j.aim.2012.07.029<\/a>.","DOI":"10.1016\/j.aim.2012.07.029"},{"key":"15","doi-asserted-by":"crossref","unstructured":"[15] A. C. M. Freitas, J. M. Freitas and M. Todd. Speed of convergence for laws of rare events and escape rates. <i>Stochastic Process. Appl.<\/i> <b>125<\/b> (4) (2015) 1653\u20131687. Available at <a href=\"arXiv:1401.4206\">arXiv:1401.4206<\/a>. <a href=\"doi:10.1016\/j.spa.2014.11.011\">doi:10.1016\/j.spa.2014.11.011<\/a>.","DOI":"10.1016\/j.spa.2014.11.011"},{"key":"16","unstructured":"[16] A. C. M. Freitas, J. M. Freitas and S. Vaienti Extreme value laws for non stationary, sequential intermittent systems. Preprint, 2016. Available at <a href=\"arXiv:1605.06287\">arXiv:1605.06287<\/a>."},{"key":"17","doi-asserted-by":"crossref","unstructured":"[17] C. Gonz\u00e1lez-Tokman, B. R. Hunt and P. Wright. Approximating invariant densities of metastable systems. <i>Ergodic Theory Dynam. Systems<\/i> <b>31<\/b> (5) (2011) 1345\u20131361. <a href=\"doi:10.1017\/S0143385710000337\">doi:10.1017\/S0143385710000337<\/a>.","DOI":"10.1017\/S0143385710000337"},{"key":"18","unstructured":"[18] N. Haydn, M. Nicol, A. T\u00f6r\u00f6k and S. Vaienti Almost sure invariance principle for sequential and non-stationary dynamical systems. Preprint. Available at <a href=\"arXiv:1406.4266\">arXiv:1406.4266<\/a>."},{"key":"19","doi-asserted-by":"crossref","unstructured":"[19] N. Haydn, M. Nicol, S. Vaienti and L. Zhang. Central limit theorems for the shrinking target problem. <i>J. Stat. Phys.<\/i> <b>153<\/b> (5) (2013) 864\u2013887. <a href=\"doi:10.1007\/s10955-013-0860-3\">doi:10.1007\/s10955-013-0860-3<\/a>.","DOI":"10.1007\/s10955-013-0860-3"},{"key":"20","doi-asserted-by":"crossref","unstructured":"[20] H. Hu and S. Vaienti. Absolutely continuous invariant measures for non-uniformly expanding maps. <i>Ergodic Theory Dynam. Systems<\/i> <b>29<\/b> (4) (2009) 1185\u20131215. <a href=\"doi:10.1017\/S0143385708000576\">doi:10.1017\/S0143385708000576<\/a>.","DOI":"10.1017\/S0143385708000576"},{"key":"21","doi-asserted-by":"crossref","unstructured":"[21] J. H\u00fcsler. Asymptotic approximation of crossing probabilities of random sequences. <i>Z. Wahrsch. Verw. Gebiete<\/i> <b>63<\/b> (2) (1983) 257\u2013270. <a href=\"doi:10.1007\/BF00538965\">doi:10.1007\/BF00538965<\/a>.","DOI":"10.1007\/BF00538965"},{"key":"22","doi-asserted-by":"crossref","unstructured":"[22] J. H\u00fcsler. Extreme values of nonstationary random sequences. <i>J. Appl. Probab.<\/i> <b>23<\/b> (4) (1986) 937\u2013950.","DOI":"10.2307\/3214467"},{"key":"23","doi-asserted-by":"crossref","unstructured":"[23] Y. Kifer. <i>Ergodic Theory of Random Transformations. Progress in Probability and Statistics<\/i> <b>10<\/b>. Birkh\u00e4user Boston, Inc., Boston, MA, 1986. <a href=\"doi:10.1007\/978-1-4684-9175-3\">doi:10.1007\/978-1-4684-9175-3<\/a>.","DOI":"10.1007\/978-1-4684-9175-3"},{"key":"24","doi-asserted-by":"crossref","unstructured":"[24] Y. Kifer. <i>Random Perturbations of Dynamical Systems. Progress in Probability and Statistics<\/i> <b>16<\/b>. Birkh\u00e4user Boston, Inc., Boston, MA, 1988. <a href=\"doi:10.1007\/978-1-4615-8181-9\">doi:10.1007\/978-1-4615-8181-9<\/a>.","DOI":"10.1007\/978-1-4615-8181-9"},{"key":"25","doi-asserted-by":"crossref","unstructured":"[25] Y. Kifer. Limit theorems for random transformations and processes in random environments. <i>Trans. Amer. Math. Soc.<\/i> <b>350<\/b> (4) (1998) 1481\u20131518. <a href=\"doi:10.1090\/S0002-9947-98-02068-6\">doi:10.1090\/S0002-9947-98-02068-6<\/a>.","DOI":"10.1090\/S0002-9947-98-02068-6"},{"key":"26","doi-asserted-by":"crossref","unstructured":"[26] Y. Kifer and A. Rapaport. Poisson and compound Poisson approximations in conventional and nonconventional setups. <i>Probab. Theory Related Fields<\/i> <b>160<\/b> (3\u20134) (2014) 797\u2013831. <a href=\"doi:10.1007\/s00440-013-0541-9\">doi:10.1007\/s00440-013-0541-9<\/a>.","DOI":"10.1007\/s00440-013-0541-9"},{"key":"27","unstructured":"[27] M. Nicol, A. T\u00f6r\u00f6k and S. Vaienti Central limit theorems for sequential and random intermittent dynamical systems. Preprint, 2015. Available at <a href=\"arXiv:1510.03214\">arXiv:1510.03214<\/a>."},{"key":"28","doi-asserted-by":"crossref","unstructured":"[28] X.-F. Niu. Extreme value theory for a class of nonstationary time series with applications. <i>Ann. Appl. Probab.<\/i> <b>7<\/b> (2) (1997) 508\u2013522. <a href=\"doi:10.1214\/aoap\/1034625342\">doi:10.1214\/aoap\/1034625342<\/a>.","DOI":"10.1214\/aoap\/1034625342"},{"key":"29","doi-asserted-by":"crossref","unstructured":"[29] W. Parry. On the $\\beta$-expansions of real numbers. <i>Acta Math. Acad. Sci. Hung.<\/i> <b>11<\/b> (1960) 401\u2013416.","DOI":"10.1007\/BF02020954"},{"key":"30","doi-asserted-by":"crossref","unstructured":"[30] J. Rousseau. Hitting time statistics for observations of dynamical systems. <i>Nonlinearity<\/i> <b>27<\/b> (9) (2014) 2377\u20132392. <a href=\"doi:10.1088\/0951-7715\/27\/9\/2377\">doi:10.1088\/0951-7715\/27\/9\/2377<\/a>.","DOI":"10.1088\/0951-7715\/27\/9\/2377"},{"key":"31","doi-asserted-by":"crossref","unstructured":"[31] J. Rousseau, B. Saussol and P. Varandas. Exponential law for random subshifts of finite type. <i>Stochastic Process. Appl.<\/i> <b>124<\/b> (10) (2014) 3260\u20133276. <a href=\"doi:10.1016\/j.spa.2014.04.016\">doi:10.1016\/j.spa.2014.04.016<\/a>.","DOI":"10.1016\/j.spa.2014.04.016"},{"key":"32","doi-asserted-by":"crossref","unstructured":"[32] J. Rousseau and M. Todd. Hitting times and periodicity in random dynamics. <i>J. Stat. Phys.<\/i> <b>161<\/b> (1) (2015) 131\u2013150. <a href=\"doi:10.1007\/s10955-015-1325-7\">doi:10.1007\/s10955-015-1325-7<\/a>.","DOI":"10.1007\/s10955-015-1325-7"},{"key":"33","doi-asserted-by":"crossref","unstructured":"[33] B. Saussol. Absolutely continuous invariant measures for multidimensional expanding maps. <i>Israel J. Math.<\/i> <b>116<\/b> (2000) 223\u2013248. <a href=\"doi:10.1007\/BF02773219\">doi:10.1007\/BF02773219<\/a>.","DOI":"10.1007\/BF02773219"}],"container-title":["Annales de l'Institut Henri Poincar\u00e9, Probabilit\u00e9s et Statistiques"],"original-title":[],"link":[{"URL":"http:\/\/projecteuclid.org\/download\/pdfview_1\/euclid.aihp\/1500624044","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T16:32:13Z","timestamp":1620318733000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/annales-de-linstitut-henri-poincare-probabilites-et-statistiques\/volume-53\/issue-3\/Extreme-Value-Laws-for-non-stationary-processes-generated-by-sequential\/10.1214\/16-AIHP757.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,1]]},"references-count":33,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,8,1]]}},"URL":"https:\/\/doi.org\/10.1214\/16-aihp757","relation":{},"ISSN":["0246-0203"],"issn-type":[{"value":"0246-0203","type":"print"}],"subject":[],"published":{"date-parts":[[2017,8,1]]}}}