Limit Theorems

  1. An invariance principle for lattices of dependent random variables and certain rates of convergence, (1972), Ph.d. Thesis. University of Wisconsin, Madison, Wisconsin.

  2. A note on the central limit theorem in Banach spaces Ann. Probability 5 (1977) 283-286.

  3. On the limit theorems for random variables with values in the spaces Lp (2<= p< infinity ), Z Wahrscheinlichkeitstheorie verw. Gebiete 41 (1978) 289-304 (with G. Pisier).

  4. On sums of independent random variables with values in Lp (2<= p < infinity), Lecture Notes in Math 709 Prob. in Banach Spaces I (1978) 111-124 (with E. Giné and V. Mandrekar).

  5. Some stability results for vector valued random variables, Ann. of Prob. 7 (1979) 75-84. (with J. Kuelbs).

  6. Central limit problem for symmetric case: Convergence to non-Gaussian laws, Studia Mathematica 67 (1980), 279-296 (with V. Mandrekar).

  7. On the accompanying law theorem in Banach spaces, Ann. Prob. 9 (1981), 202-210 (with A. Araujo, E. Giné and V. Mandrekar).

  8. Convergence to a stable distribution via order statistics, Ann. of Prob. 9 (1981), 624-632 (with R. LePage and M. Woodroofe).

  9. Some results on the LIL in Banach space with applications to weighted empirical processes, Ann. of Prob. (Special Invited Paper) 9 (1981), 713-752 (with V. Goodman and J. Kuelbs).

  10. Inequalities in Banach spaces with applications to probabilistic limit theorems-a survey, Lecture Notes in Math Springer-Verlag, Berlin 860 . For proceedings of 3rd conference on probability on Banach spaces, Tufts University, (1981), 324-239.

  11. Some additional stability results for vector valued random variables, Colloques Internationaux du C.N.R.S,. Paris 307 . Les aspects statistiques et les aspects physiques des Processus Gaussiens. (1981) 461-469 (with J. Kuelbs).

  12. Some results on LIL bahavior Ann. of Prob. 11 (1983), 506-558 (with J. Kuelbs).

  13. Central limit theorems and weak laws of large numbers in certain Banach spaces Z. Wahrscheinlichkeitstheorie verw. Gebiete 62 (1983), 323-354 (with E. Giné).

  14. Limit theorems for random sets: An application of probability in Banach space results, Probability in Banach spaces, IV (Oberwolfach 1982), Lecture Notes in Math., Springer, Berlin-New York 990 (1983) 112-135 (with E. Giné and M. Hahn).

  15. The bounded law of the iterated logarithm for the weighted empirical distribution process in the non-i.i.d. case, Ann. of Prob. 12 (1984), 335-360 (with M.Marcus).

  16. Some limit theorems for empirical processes, Ann. of Prob. 12 (1984) 929-989 (with E. Giné). Special Invited Paper.

  17. The law of large numbers for partial sum processes indexed by sets, Ann. of Prob. 15 (1985), 154-163 (with E. Giné).

  18. Lectures on the central limit theorem for empirical processes, Lecture Notes in Math. Springer, Berlin 1221 (1985-86), 50-113 (with E. Giné).

  19. Empirical processes indexed by Lipschitz functions, Ann. of Prob. 14 (1986) 1329-1338 (with E. Giné).

  20. A remark on the central limit theorem for random measures and processes, Proceedings of the IV Vilnius Conference on Probability and Mathematical Statistics, 1985, VNU Press, The Netherlands (1987) 483-487 (with E. Giné).

  21. The central limit theorem and the law of the iterated logarithm for empirical processes under local conditions, Prob. theory and Related Fields 77 (1988) 271-305 (with N. Andersen, E. Giné and M. Ossiander).

  22. The central limit theorem for empirical processes under local conditions: the case of Radon infinitely divisible limits without Gaussian component, Trans. Amer. Math. Soc. 309 (1988) 1-34 (with N. Andersen, E. Giné).

  23. Necessary conditions for the bootstrap of the mean Ann. Stat. 17 (1989) 684-691 (with E. Giné).

  24. Lp-multipliers in the central limit theorem with p-stable limit, Probability theory on vector spaces, IV 1987, Lecture Notes in Math., 1391 (1989) 74-81 (with E. Giné).

  25. Bootstrapping general empirical measures Ann. Prob. 18 (1990) 851-869 (with E. Giné).

  26. Central limit theorems for the local time of certain Markov processes and the squares of Gaussian processes, Ann. of Probab. 18 (1990) 1126-1140 (with R. Adler and M. Marcus).

  27. Universal Donsker classes and Type 2, Probability in Banach spaces, 6 (Sandbjerg, 1986, Denmark. Lecture Notes in Math., Progr. in Probab., 20 Birkhäuser, Boston (1990) 283-288.

  28. On random multipliers for the central limit theorem with p-stable limit, 0 < p < 2 Probability in Banach spaces, 6 (Sandbjerg, 1986) Progr. Probab., 20 Birkhäuser Boston (1990) 120-149 (with E. Giné and M. Marcus).

  29. Gaussian characterization of uniform Donsker classes of functions Ann. Probab. 19 (1991), 758-782 (with E. Giné).

  30. Uniform and Universal Glivenko-Cantelli Classes, Journal of theoretical probability 4 (1991) 485-510 (with R. M. Dudley, E. Giné).

  31. Marcinkiewicz type laws of large numbers and convergence of moments for U-statistics, Probability in Banach spaces ,8, Bowdoin, Maine (1991), Progr. Probab. 30 (1992) 273-291 (with E. Giné).

  32. A remark on convergence in distribution of U-statistics Ann. of Probab. 22 (1994) 117-125, (with E. Giné).

  33. Laws of large numbers for quadratic forms, maxima of products and truncated sums of i.i.d. random variables Ann. of Probab. 23 (1995) 292-333, (with J. Cuzick and E. Giné).

  34. Necessary and sufficient conditions for the strong law of large numbers for U-statistics, (with R. Latala), Ann. of Probab. 28 (2000) 1908-1924.

  35. The LIL for canonical U-statistics of order 2. (with E. Giné, R. Latala and S. Kwapien) 29 (2001) 520-557.

  36. On the limit set in the law of the iterated logarithm for U-statistics of order two (with S. Kwapien, R. Latala and K. Oleszkiewicz). High dimensional probability, III (Sandjberg, 2002), 111--126, Progr. Probab., 55, Birkhauser, Basel, 2003.

  37. Weighted uniform consistency of kernel density estimators, (with E. Giné and V. Koltchinskii). Ann. of Probab. , 32, (2004) 2570-2605.

  38. When Does a Randomly Weighted Self-normalized Sum Converge in Distribution? (D. Mason). Electronic Communications in Probability, 10, (2005) 70-81.

  39. Modified Empirical CLT's under only pre-Gaussian conditions (with S. Mendelson).IMS Lecture Notes-Monograph Series; High Dimensional Probability, 51, (2006) 173-184.

  40. Abstract of Another View of the CLT in Banach Spaces (with Jim Kuelbs), accepted in the Journal of Theoretical Probability, 37 pages.