Cuny, Christophe; Dedecker, Jerome; Korepanov, A.; Merlevède, Florence Rates in almost sure invariance principle for slowly mixing dynamical systems. (English) Zbl 1448.37008 Ergodic Theory Dyn. Syst. 40, No. 9, 2317-2348 (2020). Reviewer: George Stoica (Saint John) MSC: 37A50 37E05 60F17 60G10 PDF BibTeX XML Cite \textit{C. Cuny} et al., Ergodic Theory Dyn. Syst. 40, No. 9, 2317--2348 (2020; Zbl 1448.37008) Full Text: DOI
Cuny, Christophe; Dedecker, Jérôme; Merlevède, Florence On the Komlós, Major and Tusnády strong approximation for some classes of random iterates. (English) Zbl 1384.60071 Stochastic Processes Appl. 128, No. 4, 1347-1385 (2018). MSC: 60F17 60G10 60J05 PDF BibTeX XML Cite \textit{C. Cuny} et al., Stochastic Processes Appl. 128, No. 4, 1347--1385 (2018; Zbl 1384.60071) Full Text: DOI
Berkes, István; Liu, Weidong; Wu, Wei Biao Komlós-Major-Tusnády approximation under dependence. (English) Zbl 1308.60037 Ann. Probab. 42, No. 2, 794-817 (2014). Reviewer: Jurgita Markeviciute (Vilnius) MSC: 60F17 60G10 60J65 PDF BibTeX XML Cite \textit{I. Berkes} et al., Ann. Probab. 42, No. 2, 794--817 (2014; Zbl 1308.60037) Full Text: DOI Euclid arXiv
Zaitsev, A. Yu. The accuracy of strong Gaussian approximation for sums of independent random vectors. (English. Russian summary) Zbl 1287.60044 Russ. Math. Surv. 68, No. 4, 721-761 (2013); translation from Usp. Mat. Nauk 68, No. 4, 129-172 (2013). Reviewer: Ivan Podvigin (Novosibirsk) MSC: 60F17 60G50 PDF BibTeX XML Cite \textit{A. Yu. Zaitsev}, Russ. Math. Surv. 68, No. 4, 721--761 (2013; Zbl 1287.60044); translation from Usp. Mat. Nauk 68, No. 4, 129--172 (2013) Full Text: DOI
Portnoy, Stephen Nearly root-\(n\) approximation for regression quantile processes. (English) Zbl 1284.62291 Ann. Stat. 40, No. 3, 1714-1736 (2012). MSC: 62G20 62G30 62J99 60F17 PDF BibTeX XML Cite \textit{S. Portnoy}, Ann. Stat. 40, No. 3, 1714--1736 (2012; Zbl 1284.62291) Full Text: DOI Euclid arXiv
Sakhanenko, A. I. A general estimate in the invariance principle. (English. Russian original) Zbl 1243.60032 Sib. Math. J. 52, No. 4, 696-710 (2011); translation from Sib. Mat. Zh. 52, No. 4, 876-893 (2011). Reviewer: Tadeusz Inglot (Wrocław) MSC: 60F17 60F15 PDF BibTeX XML Cite \textit{A. I. Sakhanenko}, Sib. Math. J. 52, No. 4, 696--710 (2011; Zbl 1243.60032); translation from Sib. Mat. Zh. 52, No. 4, 876--893 (2011) Full Text: DOI
Götze, F.; Zaitsev, A. Yu. Bounds for the rate of strong approximation in the multidimensional invariance principle. (English. Russian original) Zbl 1196.60053 Theory Probab. Appl. 53, No. 1, 59-80 (2009); translation from Teor. Veroyatn. Primen. 53, No. 1, 100-123 (2008). Reviewer: Ken-ichi Yoshihara (Tokyo) MSC: 60F17 60F15 PDF BibTeX XML Cite \textit{F. Götze} and \textit{A. Yu. Zaitsev}, Theory Probab. Appl. 53, No. 1, 59--80 (2009; Zbl 1196.60053); translation from Teor. Veroyatn. Primen. 53, No. 1, 100--123 (2008) Full Text: DOI
Csörgő, Miklós A glimpse of the KMT (1975) approximation of empirical processes by Brownian bridges via quantiles. (English) Zbl 1135.60312 Acta Sci. Math. 73, No. 1-2, 349-366 (2007). MSC: 60F17 60F15 60G50 62G30 PDF BibTeX XML Cite \textit{M. Csörgő}, Acta Sci. Math. 73, No. 1--2, 349--366 (2007; Zbl 1135.60312)
Sakhanenko, A. I. Estimates in the invariance principle in terms of truncated power moments. (Russian, English) Zbl 1150.60364 Sib. Mat. Zh. 47, No. 6, 1355-1371 (2006); translation in Sib. Math. J. 47, No. 6, 1113-1127 (2006). MSC: 60F17 60F05 60F10 60G50 PDF BibTeX XML Cite \textit{A. I. Sakhanenko}, Sib. Mat. Zh. 47, No. 6, 1355--1371 (2006; Zbl 1150.60364); translation in Sib. Math. J. 47, No. 6, 1113--1127 (2006) Full Text: EMIS EuDML
Zhyrnyj, George G. Normal approximation of multiple sums of independent random variables with given laws. (English) Zbl 1064.60055 Theory Stoch. Process. 7(23), No. 3-4, 131-136 (2001). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 60F99 60G50 60G60 PDF BibTeX XML Cite \textit{G. G. Zhyrnyj}, Theory Stoch. Process. 7(23), No. 3--4, 131--136 (2001; Zbl 1064.60055)
Zaitsev, A. Yu. On the strong Gaussian approximation in multidimensional case. (English) Zbl 1055.60032 Ann. I.S.U.P. 45, No. 2-3, 3-7 (2001). MSC: 60F17 60F15 PDF BibTeX XML Cite \textit{A. Yu. Zaitsev}, Ann. I.S.U.P. 45, No. 2--3, 3--7 (2001; Zbl 1055.60032)
Rio, Emmanuel Strong approximation for set-indexed partial sum processes via KMT constructions. III. (English) Zbl 0930.60016 ESAIM, Probab. Stat. 1, 319-338 (1997). MSC: 60F15 PDF BibTeX XML Cite \textit{E. Rio}, ESAIM, Probab. Stat. 1, 319--338 (1997; Zbl 0930.60016) Full Text: DOI Link EuDML
Zhang, Hanqin; Hsu, Guang-Hui A new proof of the invariance principle for renewal processes. (English) Zbl 0842.60031 Sankhyā, Ser. A 56, No. 2, 375-378 (1994). Reviewer: J.Steinebach (Marburg) MSC: 60F17 60K05 PDF BibTeX XML Cite \textit{H. Zhang} and \textit{G.-H. Hsu}, Sankhyā, Ser. A 56, No. 2, 375--378 (1994; Zbl 0842.60031)
Horváth, Lajos Strong approximations of open queueing networks. (English) Zbl 0758.60099 Math. Oper. Res. 17, No. 2, 487-508 (1992). Reviewer: T.Inglot (Wrocław) MSC: 60K25 60F17 60K20 60K10 PDF BibTeX XML Cite \textit{L. Horváth}, Math. Oper. Res. 17, No. 2, 487--508 (1992; Zbl 0758.60099) Full Text: DOI
Massart, Pascal Strong approximation for multivariate empirical and related processes, via KMT constructions. (English) Zbl 0675.60026 Ann. Probab. 17, No. 1, 266-291 (1989). Reviewer: P.Revesz MSC: 60F17 60G50 60G60 62E20 62G30 PDF BibTeX XML Cite \textit{P. Massart}, Ann. Probab. 17, No. 1, 266--291 (1989; Zbl 0675.60026) Full Text: DOI
Russo, Ralph P. Strong laws for quantiles corresponding to moving blocks of random variables. (English) Zbl 0636.60028 Ann. Probab. 16, No. 1, 162-171 (1988). Reviewer: A.R.Dabrowski MSC: 60F15 62G30 PDF BibTeX XML Cite \textit{R. P. Russo}, Ann. Probab. 16, No. 1, 162--171 (1988; Zbl 0636.60028) Full Text: DOI
Mason, David M.; van Zwet, Willem R. A refinement of the KMT inequality for the uniform empirical process. (English) Zbl 0638.60040 Ann. Probab. 15, 871-884 (1987). Reviewer: F.Götze MSC: 60F15 60G17 PDF BibTeX XML Cite \textit{D. M. Mason} and \textit{W. R. van Zwet}, Ann. Probab. 15, 871--884 (1987; Zbl 0638.60040) Full Text: DOI
Christoph, Gerd Strong approximations for partial sums of random variables attracted to a stable law. (English) Zbl 0635.60029 Math. Nachr. 134, 289-294 (1987). Reviewer: A.R.Dabrowski MSC: 60F15 60F17 PDF BibTeX XML Cite \textit{G. Christoph}, Math. Nachr. 134, 289--294 (1987; Zbl 0635.60029) Full Text: DOI
Csörgö, Miklós; Horváth, Lajos; Steinebach, Josef Strong approximations for renewal processes. (English) Zbl 0601.60030 C. R. Math. Acad. Sci., Soc. R. Can. 8, 151-154 (1986). Reviewer: A.Dabrowski MSC: 60F15 60F17 60K05 PDF BibTeX XML Cite \textit{M. Csörgö} et al., C. R. Math. Acad. Sci., Soc. R. Can. 8, 151--154 (1986; Zbl 0601.60030)
Steinebach, J. Some remarks on strong approximations and the Hansen-Russo law of large numbers. (English) Zbl 0594.60037 Stat. Decis. 4, 237-249 (1986). Reviewer: A.Dabrowski MSC: 60F15 60G50 60F17 60J65 PDF BibTeX XML Cite \textit{J. Steinebach}, Stat. Decis. 4, 237--249 (1986; Zbl 0594.60037)
Sakhanenko, A. I. Convergence rate in the invariance principle for non-identically distributed variables with exponential moments. (English) Zbl 0591.60027 Advances in probability theory: Limit theorems for sums of random variables, Transl. Ser. Math. Eng., 2-73 (1986). MSC: 60F15 60F17 PDF BibTeX XML
Steinebach, Josef On certain limits of strong invariance principles. (English) Zbl 0648.60034 Bull. Soc. Math. Belg., Sér. A 37, 89-99 (1985). MSC: 60F15 60F17 60F10 60G50 60J65 PDF BibTeX XML Cite \textit{J. Steinebach}, Bull. Soc. Math. Belg., Sér. A 37, 89--99 (1985; Zbl 0648.60034)
Sakhanenko, A. I. Estimates in the invariance principle. (Russian) Zbl 0585.60044 Predel’nye Teoremy Teorii Veroyatnostej, Tr. Inst. Mat. 5, 27-44 (1985). Reviewer: T.Inglot MSC: 60F17 60J65 60F15 60G50 PDF BibTeX XML
Steinebach, J. Between invariance principles and Erdős-Rényi laws. (English) Zbl 0578.60025 Limit theorems in probability and statistics, 2nd Colloq., Veszprém/Hung. 1982, Vol. II, Colloq. Math. Soc. János Bolyai 36, 981-1005 (1984). MSC: 60F15 60F10 60F17 60K05 PDF BibTeX XML
Sakhanenko, A. I. The convergence rate in the invariance principle for differently distributed variables with exponential moments. (Russian) Zbl 0541.60024 Predel’nye Teoremy dlya Summ Sluchajnykh Velichin, Tr. Inst. Mat. 3, 4-49 (1984). Reviewer: K.Kubilius MSC: 60F15 60F17 PDF BibTeX XML
Sahanenko, A. On unimprovable estimates of the rate of convergence in invariance principle. (English) Zbl 0518.60046 Nonparametric statistical inference, Budapest 1980, Vol. II, Colloq. Math. Soc. Janos Bolyai 32, 779-784 (1982). MSC: 60F17 PDF BibTeX XML
Shorack, Galen R. Kiefer’s theorem via the Hungarian construction. (English) Zbl 0501.60038 Z. Wahrscheinlichkeitstheor. Verw. Geb. 61, 369-373 (1982). MSC: 60F15 60G17 PDF BibTeX XML Cite \textit{G. R. Shorack}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 61, 369--373 (1982; Zbl 0501.60038) Full Text: DOI
Csörgö, M.; Révész, P. Strong approximations in probability and statistics. (English) Zbl 0539.60029 Probability and Mathematical Statistics. New York-San Francisco-London: Academic Press, a Subsidiary of Harcourt Brace Jovanovich, Publishers; Budapest: Akadémiai Kiadó. 284 p. $ 35.50 (1981). Reviewer: E.Bolthausen MSC: 60F15 60F05 60-02 PDF BibTeX XML