{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T11:15:58Z","timestamp":1649157358851},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,4,22]],"date-time":"2016-04-22T00:00:00Z","timestamp":1461283200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003549","name":"OTKA","doi-asserted-by":"crossref","award":["K108615"],"award-info":[{"award-number":["K108615"]}],"id":[{"id":"10.13039\/501100003549","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s10998-016-0135-2","type":"journal-article","created":{"date-parts":[[2016,4,22]],"date-time":"2016-04-22T14:00:44Z","timestamp":1461333644000},"page":"208-223","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Strong approximations for long memory sequences based partial sums, counting and their Vervaat processes"],"prefix":"10.1007","volume":"73","author":[{"given":"Endre","family":"Cs\u00e1ki","sequence":"first","affiliation":[]},{"given":"Mikl\u00f3s","family":"Cs\u00f6rg\u0151","sequence":"additional","affiliation":[]},{"given":"Rafa\u0142","family":"Kulik","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,4,22]]},"reference":[{"key":"135_CR1","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1214\/aoms\/1177699450","volume":"37","author":"RR Bahadur","year":"1966","unstructured":"R.R. Bahadur, A note on quantiles in large samples. Ann. Math. Stat. 37, 577\u2013580 (1966)","journal-title":"Ann. Math. Stat."},{"key":"135_CR2","first-page":"145","volume-title":"Dependence in Probability, Analysis and Number Theory","author":"E Cs\u00e1ki","year":"2010","unstructured":"E. Cs\u00e1ki, M. Cs\u00f6rg\u0151, R. Kulik, On Vervaat processes for sums and renewals in weakly dependent cases, in Dependence in Probability, Analysis and Number Theory, ed. by I. Berkes, R. Bradley, H. Dehling, M. Peligrad, R. Tichy (Kendrick Press, Heber City, 2010), pp. 145\u2013156"},{"issue":"3","key":"135_CR3","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1016\/j.jspi.2006.06.019","volume":"137","author":"E Cs\u00e1ki","year":"2007","unstructured":"E. Cs\u00e1ki, M. Cs\u00f6rg\u0151, Z. Rychlik, J. Steinebach, On Vervaat and Vervaat-error-type processes for partial sums and renewals. J. Stat. Plan. Inference 137(3), 953\u2013966 (2007)","journal-title":"J. Stat. Plan. Inference"},{"issue":"3\u20134","key":"135_CR4","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s00440-007-0107-9","volume":"142","author":"M Cs\u00f6rg\u0151","year":"2008","unstructured":"M. Cs\u00f6rg\u0151, R. Kulik, Reduction principles for quantile and Bahadur\u2013Kiefer processes of long-range dependent linear sequences. Probab. Theory Relat. Fields 142(3\u20134), 339\u2013366 (2008)","journal-title":"Probab. Theory Relat. Fields"},{"key":"135_CR5","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1214\/aop\/1176994994","volume":"7","author":"M Cs\u00f6rg\u0151","year":"1979","unstructured":"M. Cs\u00f6rg\u0151, P. R\u00e9v\u00e9sz, How big are the increments of a Wiener process? Ann. Probab. 7, 731\u2013737 (1979)","journal-title":"Ann. Probab."},{"key":"135_CR6","volume-title":"Strong Approximations in Probability and Statistics","author":"M Cs\u00f6rg\u0151","year":"1981","unstructured":"M. Cs\u00f6rg\u0151, P. R\u00e9v\u00e9sz, Strong Approximations in Probability and Statistics (Academic Press, New York, 1981)"},{"issue":"3","key":"135_CR7","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1007\/s10959-007-0124-8","volume":"21","author":"M Cs\u00f6rg\u0151","year":"2008","unstructured":"M. Cs\u00f6rg\u0151, R. Kulik, Weak convergence of Vervaat and Vervaat error processes of long-range dependent sequences. J. Theor. Probab. 21(3), 672\u2013686 (2008)","journal-title":"J. Theor. Probab."},{"issue":"2","key":"135_CR8","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1214\/009053606000000164","volume":"34","author":"M Cs\u00f6rg\u0151","year":"2006","unstructured":"M. Cs\u00f6rg\u0151, B. Szyszkowicz, L.H. Wang, Strong invariance principles for sequential Bahadur\u2013Kiefer and Vervaat error processes of long-range dependent sequences. Ann. Stat. 34(2), 1013\u20131044 (2006)","journal-title":"Ann. Stat."},{"key":"135_CR9","doi-asserted-by":"crossref","unstructured":"M. Cs\u00f6rg\u0151, B. Szyszkowicz, L.H. Wang, Correction: \u201cStrong invariance principles for sequential Bahadur-Kiefer and Vervaat error processes of long-range dependent sequences\u201d [Ann. Stat. 34(2), 1013\u20131044 (2006)]. Ann. Stat., 35(6):2815\u20132817 (2007)","DOI":"10.1214\/009053607000000370"},{"issue":"4","key":"135_CR10","doi-asserted-by":"crossref","first-page":"1767","DOI":"10.1214\/aos\/1176347394","volume":"17","author":"H Dehling","year":"1989","unstructured":"H. Dehling, M.S. Taqqu, The empirical process of some long-range dependent sequences with an application to $$U$$ U -statistics. Ann. Stat. 17(4), 1767\u20131783 (1989)","journal-title":"Ann. Stat."},{"issue":"1","key":"135_CR11","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0304-4149(84)90166-2","volume":"18","author":"L Horv\u00e1th","year":"1984","unstructured":"L. Horv\u00e1th, Strong approximation of renewal processes. Stoch. Process. Appl. 18(1), 127\u2013138 (1984)","journal-title":"Stoch. Process. Appl."},{"issue":"1\u20132","key":"135_CR12","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF01949120","volume":"47","author":"L Horv\u00e1th","year":"1986","unstructured":"L. Horv\u00e1th, Strong approximations of renewal processes and their applications. Acta Math. Hung. 47(1\u20132), 13\u201328 (1986)","journal-title":"Acta Math. Hung."},{"key":"135_CR13","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1214\/aoms\/1177698690","volume":"38","author":"J Kiefer","year":"1967","unstructured":"J. Kiefer, On Bahadur\u2019s representation of sample quantiles. Ann. Math. Stat. 38, 1323\u20131342 (1967)","journal-title":"Ann. Math. Stat."},{"key":"135_CR14","unstructured":"J. Kiefer, Deviations between the sample quantile process and the sample $$\\text{ df }$$ df , in: Nonparametric Techniques in Statistical Inference (Proc. Sympos., Indiana Univ., Bloomington, Ind., 1969), (Cambridge Univ. Press, London, 1970), pp. 299\u2013319"},{"key":"135_CR15","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/BF00533093","volume":"32","author":"J Koml\u00f3s","year":"1975","unstructured":"J. Koml\u00f3s, P. Major, G. Tusn\u00e1dy, An approximation of partial sums of independent $$\\text{ RV }$$ RV \u2019s and the sample $$\\text{ DF }$$ DF . I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 32, 111\u2013131 (1975)","journal-title":"I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete"},{"issue":"1","key":"135_CR16","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/BF00532688","volume":"34","author":"J Koml\u00f3s","year":"1976","unstructured":"J. Koml\u00f3s, P. Major, G. Tusn\u00e1dy, An approximation of partial sums of independent RV\u2019s, and the sample DF. II. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 34(1), 33\u201358 (1976)","journal-title":"II. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete"},{"key":"135_CR17","doi-asserted-by":"crossref","unstructured":"N. K\u00f4no, Classical limit theorems for dependent random sequences having moment conditions, in Probability theory and mathematical statistics (Tbilisi, 1982), volume 1021 of Lecture Notes in Math., (Springer, Berlin, 1983), pp. 315\u2013319","DOI":"10.1007\/BFb0072927"},{"issue":"1","key":"135_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00533812","volume":"51","author":"TL Lai","year":"1980","unstructured":"T.L. Lai, W. Stout, Limit theorems for sums of dependent random variables. Z. Wahrsch. Verw. Gebiete 51(1), 1\u201314 (1980)","journal-title":"Z. Wahrsch. Verw. Gebiete"},{"issue":"2","key":"135_CR19","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF01375823","volume":"101","author":"D Monrad","year":"1995","unstructured":"D. Monrad, H. Rootz\u00e9n, Small values of Gaussian processes and functional laws of the iterated logarithm. Probab. Theory Relat. Fields 101(2), 173\u2013192 (1995)","journal-title":"Probab. Theory Relat. Fields"},{"key":"135_CR20","doi-asserted-by":"crossref","unstructured":"H. Oodaira, Some limit theorems for the maximum of normalized sums of weakly dependent random variables, in Proc. Third Japan-USSR Symposium on Probability Theory (Tashkent, 1975), Lecture Notes in Math. (Springer, Berlin, Vol. 550, 1976), pp. 443\u2013451","DOI":"10.1007\/BFb0077509"},{"key":"135_CR21","unstructured":"S. Orey, Growth rate of certain Gaussian processes, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (University of California, Berkeley, California, 1970\/1971), Vol. II: Probability theory, (Berkeley, California, University of California Press, 1972), pp. 443\u2013451"},{"issue":"1","key":"135_CR22","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0304-4149(84)90160-1","volume":"18","author":"J Ortega","year":"1984","unstructured":"J. Ortega, On the size of the increments of nonstationary Gaussian processes. Stoch. Process. Appl. 18(1), 47\u201356 (1984)","journal-title":"Stoch. Process. Appl."},{"key":"135_CR23","doi-asserted-by":"crossref","unstructured":"M.S. Taqqu, Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 31, 287\u2013302 (1974\/1975)","DOI":"10.1007\/BF00532868"},{"issue":"3","key":"135_CR24","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF00736047","volume":"40","author":"MS Taqqu","year":"1977","unstructured":"M.S. Taqqu, Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 40(3), 203\u2013238 (1977)","journal-title":"Z. Wahrscheinlichkeitstheorie und Verw. Gebiete"},{"key":"135_CR25","first-page":"5","volume-title":"Theory and Applications of Long-range Dependence","author":"MS Taqqu","year":"2003","unstructured":"M.S. Taqqu, Fractional Brownian motion and long-range dependence, in Theory and Applications of Long-range Dependence, ed. by P. Doukhan, G. Oppenheim, M.S. Taqqu (Birkh\u00e4use, Boston, 2003), pp. 5\u201338"},{"key":"135_CR26","unstructured":"W. Vervaat, Success epochs in Bernoulli trials (with applications in number theory). Mathematisch Centrum, Amsterdam. Mathematical Centre Tracts, No. 42 ( 1972)"},{"key":"135_CR27","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BF00532510","volume":"23","author":"W Vervaat","year":"1972","unstructured":"W. Vervaat, Functional central limit theorems for processes with positive drift and their inverses. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 23, 245\u2013253 (1972)","journal-title":"Z. Wahrscheinlichkeitstheorie und Verw. Gebiete"},{"issue":"2","key":"135_CR28","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1023\/A:1023570510824","volume":"16","author":"QY Wang","year":"2003","unstructured":"Q.Y. Wang, Y.X. Lin, C.M. Gulati, Strong approximation for long memory processes with applications. J. Theoret. Probab. 16(2), 377\u2013389 (2003)","journal-title":"J. Theoret. Probab."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-016-0135-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10998-016-0135-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-016-0135-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-016-0135-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T19:12:07Z","timestamp":1589656327000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10998-016-0135-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,22]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["135"],"URL":"https:\/\/doi.org\/10.1007\/s10998-016-0135-2","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,22]]}}}