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Publications of Alfredas Račkauskas

Recent publications [1996, 2002]

Earlier publications [1979, 1995]

Papers in Conference proceedings

Recent publications, [1996, 2003]

A. Račkauskas, Ch. Suquet, Necessary and sufficient condition for the Lamperti invariance principle. Teor. Imovirnost. Ta. Matem. Statyst., 68, 115-124 (2003).
A. Račkauskas, Ch. Suquet, Invariance principle under self-normalization for nonidentically distributed random variables. Acta Appl. Math. 79, No.1-2, 83-103 (2003).
A. Račkauskas, Ch. Suquet, Principe d’invariance Holderien pour des tableaux triangulaires de variables aleatoires. Liet. Matem. Rink. 43, 513-532 (2003).
A. Račkauskas, Ch. Suquet, Holder convergence of multivariate empirical characteristic functions. Math. Methods in Stat., 11 (3), 341-357 (2002).
A. Laukaitis, A. Račkauskas, Functional data analysis of payment systems.
Nonlinear Anal. Model. Contr. 7, No.2, 53-68 (2002).
A. Laukaitis, A. Račkauskas, Testing changes in Hilbert space autoregressive models. (Russian,English) Lith. Math. J. 42, No.4, 343-354 (2002); translation from Liet. Mat. Rink. 42, No.4, 434-447 (2002).
Račkauskas, A. and Suquet Ch. On Holderian functional central limit theorem for iid random elements in Banach spaces, Berkes, I. Et al. (eds.). Limit theorems in probability and statistics. Fourth Hungarian colloquium on limit theorems in probability and statistics. Balatonlelle, Hungaly, June 28-July 2, 1999. Vol. II (2002), 485-498.
Račkauskas, A. and Gotze, F. Adaptive choise of bootstrap sample sizes, In: State of the Art in Probability and Statistics. Festschrift for W. R. van Zwet, I.M.S. Lecture Notes-monograph series, 2001, 36, 286-309.
Račkauskas, A. and Suquet Ch. Invariance principles for adaptive self-normalized partial sums processes. Stoch. Proc. Appl., 41 (2001), no. 1, 65 – 71.
Račkauskas, A. and Suquet Ch. Holder version of Banach space valued random fields. Georgian Math. J., 8 (2001), no. 2, 347 – 362.
Davydov, Yu.; Paulauskas, V.; Račkauskas, A. More on P-stable convex sets in Banach spaces. J. Theoret. Probab. 13 (2000), no. 1, 39 - 64.
Bloznelis, M.; Račkauskas, A. A Berry-Esseen bound for least squares error variance estimators of regression parameters. Liet. Mat. Rink. 39 (1999), no. 1,1 - 8; translation in Lithuanian Math. J. 39 (1999), no. 1, 1 - 7 62J05 (60F05 62F12)
Račkauskas, Alfredas Large deviations behavior for the quadratic error of density estimate. Limit theorems of probability theory (Vilnius, 1999). Acta Appl. Math. 58 (1999), no. 1-3, 237 - 246.
Račkauskas, Alfredas; Suquet, Charles. Central limit theorem in Hölder spaces. Probab. Math. Statist. 19 (1999), no. 1, 133 - 152.
Leipus, R.; Račkauskas, A. Security price modelling by a binomial tree. Appl. Math. (Warsaw) 26 (1999), no. 3, 253 - 266. 91B28 (62M10)
Račkauskas, A. and Suquet Ch. Random fields and central limit theorem in some generalized Holder spaces. In: Probability Theory and Mathematical Statistics: Proceedings of the Seventh Vilnius Conference (1998), Eds. B. Grigelionis et al., VSP/TEV. Utrecht/Vilnius, 1999, 599 – 671.
Račkauskas, A. Limit theorems for large deviations probabilities of certain quadratic forms. Liet. Mat. Rink. 37 (1997), no. 4,532 - 549; translation in Lithuanian Math. J. 37 (1997), no. 4, 402 - 415 (1998).
Račkauskas A. Limit theorems for large deviations probabilities of certain quadratic forms. Lithuanian Math. J. yr. 1997 vol. 37 pages 402 - 415
Kubilius, K.; Račkauskas, A. On the asymptotic normality of estimates in almost nonstationary {\rm AR}(1) models. (Russian) Liet. Mat. Rink. 36 (1996), no. 4,441 - 463; translation in Lithuanian Math. J. 36 (1996), no. 4, 352 - 370 (1997) (Reviewer: Vladimir Zaiats) 62M10 (62F12)
Kubilius, K.; Račkauskas, A. On the asymptotic accuracy of least-squares estimators in nearly unstable {\rm AR}(1) processes. Math. Methods Statist. 5 (1996), no. 4, 464 - 476. (Reviewer: Wolfgang Schmid) 62M10 (62L12)
Račkauskas, A. Asymptotic accuracy of the least-squares estimates in nearly nonstationary autoregressive models. Liet. Mat. Rink. 36 (1996), no. 1,115 - 129; translation in Lithuanian Math. J. 36 (1996), no. 1, 92 - 103 (Reviewer: Hartmut Milbrodt) 62M10 (62F10)

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Earlier publications [1979, 1995]

Papers in Journals

1. Račkauskas, Alfredas On the rate of convergence in the martingale CLT. Statist. Probab. Lett. 23 (1995), no. 3, 221 - 226. (Reviewer: M. Csörgö) 60B12 (60F05 60G42)

2. Račkauskas, A. On the conditional covariance condition in the martingale CLT. Liet. Mat. Rink. 35 (1995), no. 1,118 - 131; translation in Lithuanian Math. J. 35 (1995), no. 1, 93 - 104 60F05 (60B12)

3. Račkauskas, A. Large deviations for martingales with some applications. Acta Appl. Math. 38 (1995), no. 1, 109 - 129. (Reviewer: Erich Haeusler) 60F10 (60G42)

4. Račkauskas, A. On Gaussian approximation of Hilbert space valued discrete time martingales. Liet. Mat. Rink. 33 (1993), no. 4,476 - 491; translation in Lithuanian Math. J. 33 (1993), no. 4, 368 - 380 (1994) (Reviewer: A. Ya. Dorogovtsev) 60B12 (60F05)

5. Račkauskas, A. On the convergence rate in martingale CLT in Hilbert spaces. Litovsk. Mat. Sb. 31 (1991), no. 3,497 - 512; translation in Lithuanian Math. J. 31 (1991), no. 3, 345 - 355 (1992) (Reviewer: Xiang Chen Wang) 60B12 (60F05 60G42)

6. Račkauskas, A. Uniform bounds in the central limit theorem for C(S) valued martingales. Litovsk. Mat. Sb. 31 (1991), no. 1,146 - 165; translation in Lithuanian Math. J. 31 (1991), no. 1, 103 - 116 (1992) (Reviewer: Adhir K. Basu) 60B12 (60G42)

7. Paulauskas, V.; Račkauskas, A. Nonuniform estimates in the central limit theorem in Banach spaces. Litovsk. Mat. Sb. 31 (1991), no. 3,483 - 496; translation in Lithuanian Math. J. 31 (1991), no. 3, 335 - 344 (1992) (Reviewer: Igor S. Borisov) 60B12

8. Račkauskas, A. On probabilities of large deviations for martingales. Litovsk. Mat. Sb. 30 (1990), no. 4,784 - 795; translation in Lithuanian Math. J. 30 (1990), no. 4, 376 - 384 (1991) (Reviewer: Xiang Chen Wang) 60G42 (60F10)

9. Bentkus, V.; Račkauskas, A. On probabilities of large deviations in Banach spaces. Probab. Theory Related Fields 86 (1990), no. 2, 131 - 154. (Reviewer: Marek Slaby) 60B12 (60F10)

10. Rachkauskas, A. Yu. Probabilities of large deviations in Linnik zones in a Hilbert space. (Russian) Litovsk. Mat. Sb. 28 (1988), no. 3,520 - 533; translation in Lithuanian Math. J. 28 (1988), no. 3, 239 - 248 (Reviewer: S. A. Book) 60B12 (60F10)

11. Rachkauskas, A. Yu. Rate of convergence in a martingale central limit theorem in the space C(S). (Russian) Litovsk. Mat. Sb. 27 (1987), no. 3, 523 - 534. (Reviewer: Yu. S. Mishura) 60G05 (60F15 60G42)

12. Bentkus V. and Račkauskas A. Estimates of the distance between sums of independent random elements in Banach spaces. Theory Probab. Appl. yr. 1984 vol. 29 lang. Russian pages 50 - 65

13. Norvaiša R. and Račkauskas A. The law of large numbers with respect to quasinorm. II. Lietuvos Matem. Rink. vol. 24 yr.1984 lang. Russian pages 162 - 176

14. Norvaiša R. and Račkauskas A. The law of large numbers with respect to quasinorms. I. Lietuvos Matem. Rink. vol. 24 yr. 1984 lang. Russian pages 130 - 144

15. Račkauskas A. An operator ideal of type (p, q) yr. 1984 vol. 24 lang. Russian Lietuvos Matem. Rink. pages 151 - 166

16. Paulauskas V. and Račkauskas A. Operators of stable type. Dokl. Akad. Nauk SSSR yr. 1984 vol. 275 (Russian) p. 306 - 310

17. Račkauskas A. On the laws of large numbers in Banach spaces. Lietuvos Matem. Rink. yr. 1983 vol. 23 lang. Russian pages 109 - 116

18. Paulauskas V., Račkauskas A. and Sakalauskas V. The central limit theorem in the space of sequences that converge to zero. Lietuvos Matem. Rink.yr. 1983 vol. 23 lang. Russian pages 163 - 174

19. Bentkus V. and Račkauskas A. Estimates of the rate of convergence of independent random variables in a Banach space.II. Lithuanian Math. J. vol. 23 yr.1983 pages 344 - 352

20. Bentkus V. and Račkauskas A. Estimates of the rate of convergence of sums of independent random variables in a Banach space.I. Lithuanian Math. J. vol. 23 yr. 1983 pages 223 - 234

21. Bentkus V. and Račkauskas A. Estimates for the rate of convergence in the central limit theorem in Prokhorov's metric. Dokl. Akad. Nauk SSSR vol. 264 yr. 1982 lang. Russian pages 521 - 524

22. Bentkus V. and Račkauskas A. On the rate of convergence in the central limit theorem in infinite-dimen\-sional spaces. Lithuanian Math. J. yr.1982 vol. 21 lang. Russian pages 271 - 276

23. Račkauskas A. and Sakalauskas V. A nonuniform estimate of the rate of convergence to stable laws in some Banach spaceslang. Russian yr. 1981 vol. 21 lang. Russian pages 185 - 193

24. Paulauskas V. and Račkauskas A. On infinitely divisible and stable laws in separable Banach spaces. II. Lietuvos Matem. Rink. yr. 1980 vol. 20 lang. Russian pages 97 - 113

25. Račkauskas A. A family of stable measures in some Banach spaces. Lietuvos Matem. Rink. vol. 20 yr. 1980 lang. Russian
pages 133 - 145

26. Račkauskas A. Asymptotic analysis of probability measures in Banach spaces. Lietuvos Matem. Rink. vol. 20 yr. 1980 lang. Russian
pages 99 - 106

27. Borovskih J. and Račkauskas A. Asymptotic behavior of distributions in Banach spaces. Lietuvos Matem. Rink. yr. 1979 vol. 19 lang. Russian pages 39 - 54

28. Račkauskas A. A remark on stable measures on Banach spaces. Lietuvos Matem. Rink. vol. 19 yr. 1979 lang. Russian
pages 161 - 165

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Papers in Conference Proceedings

1. Račkauskas, A. On the convergence rate in the multi-dimensional martingale CLT. Probability theory and mathematical statistics (Vilnius, 1993), 629 - 643, TEV, Vilnius, 1994. 60F05 (60G42)

2. Račkauskas, Alfredas On probabilities of large deviations for martingales in Hilbert spaces. Probability theory and mathematical statistics (Tokyo, 1995), 423 - 437, World Sci. Publishing, River Edge, NJ, 1996. (Reviewer: Xia Chen) 60F10 (60B11 60G42)

3. Račkauskas, A. On a multidimensional martingale with given conditional covariance structure. Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I (Eger, 1994). J. Math. Sci. 76 (1995), no. 2, 2330 - 2334. 60G42 (60F05)

4. Rackauskas, A. J. On the martingale central limit theorem in Banach spaces. Probability theory on vector spaces, IV (\L a\'ncut, 1987), 329 - 336, Lecture Notes in Math., 1391, Springer, Berlin, 1989. (Reviewer: Ireneusz Szyszkowski) 60B12 (60F05 60G42)

5. Norvaiša, R.; Paulauskas, V. J.; Račkauskas, A. An operator approach in limit theorems for sums of the type n\sp {-1/p}S\sb n in Banach spaces. Probability theory and mathematical statistics, Vol. II (Vilnius, 1985), 409 - 420, VNU Sci. Press, Utrecht, 1987. 60B12 (46B20 47B99)

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Books and Book Chapters

1. Bentkus, V.; Gettse, F.; Paulauskas, V.; Rachkauskas, A. The accuracy of Gaussian approximation in Banach spaces. (Russian) Probability theory, 6 (Russian), 39 - 139, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1991. (Reviewer: Vladimir I. Chebotarev) 60B12 (60F15)

2. Paulauskas, V.; Račkauskas, A. Approximation theory in the central limit theorem. Exact results in Banach spaces. Translated from the Russian by B. Svecevičius and Paulauskas. Mathematics and its Applications (Soviet Series), 32. Kluwer Academic Publishers Group, Dordrecht, 1989. xviii+156 pp. ISBN: 90-277-2825-9 60B12

3. Paulauskas, V. I.; Rachkauskas, A. Yu. {\cyr Tochnost\cprime approksimatsii v tsentral\cprime no\u\i predel\cprime no\u\i teoreme v banakhovykh prostranstvakh}. (Russian) [The accuracy of approximation in the central limit theorem in Banach spaces] ``Mokslas'', Vilnius, 1987. 188 pp. (Reviewer: R. M. Dudley) 60B12