Lista publikacji

  1. T. K. Krajka and Z. Rychlik, The limiting behaviour of sums and maximums of i.i.d random variables from the viewpoint of different observators, Probability and Mathematical Statistics (in print).
  2. Z. Rychlik and K. S. Szuster, On the random functional central limit theorems with almost sure convergence for subsequences, Demonstratio Mathematica, Vol. XLV, No 2, 2012, 283 – 296; Dedicated to Professor Agnieszka Plucińska on the occasion of her 80th birthday.
  3. T. K. Krajka and Z. Rychlik, Limit theorems for products of sums of independent random variables, Probability and Mathematical Statistics, Vol. 30, Fasc. 1(2010), pp. 73 – 85.
  4. T. K. Krajka and Z. Rychlik, The speed of convergence of random products of sums of independent random variables, Journal of  Mathematics and Applications, No 31, 2009, pp. 63 –78.
  5. E. B. Czerebak-Mrozowicz,  Z. Rychlik and M. Urbanek, Almost sure functional central limit theorems for multiparameters stochastic processes, Condensed Matter Physics, 2008, Vol. 11, No 2(54), pp. 371 – 381.
  6. Z. Rychlik, W. Skublewski and T. Walczynski, On the random functional central limit theorems in L2[0,1] with almost sure convergence, Acta Sci. Math. (Szeged), 73(2007), pp. 745 – 765.
  7. M. Orzóg, Z. Rychlik, On the random functional central limit theorems with almost sure convergence, Probability and Mathematical Statistics, Vol. 27, Fasc. 1(2007), pp. 125 – 138.
  8. E. Csaki, M. Csorgo, Z. Rychlik, J. Steinebach, On Vervaat and Vervaat-error type processes for partial sums and renewals, Journal of Statistical Planning and Inference, Dedicated to Madan  Lal  Puri in appreciation of his work, Vol. 137, Issue 3, pp.953 – 966.
  9. I. Fazekas and Z. Rychlik, Almost sure limit theorems for semi-selfsimilar processes, Probability and Mathematical Statistics, Vol. 25, Fasc. 2(2005), pp. 241 – 255.
  10. I. Ćwiklińska, Z. Rychlik, Weak convergence of random sums and maximum random sums under nonrandom norming, Fields Institute Communications, Vol. 44, 2004, 245 – 263.
  11. Z. Rychlik, K. S. Szuster,  Some remarks on the almost central limit theorem for independent random variables, Probability and Mathematical Statistics, Vol. 23, Fasc. 2(2003), pp. 241-249.
  12. I. Fazekas,  Z. Rychlik, Almost sure central limit theorems for random fields, Math. Nachr. 259, (2003), 12 – 18.
  13. Z. Rychlik, K. S. Szuster, On strong versions of the central limit theorem, Statistics&Probability Letters, 61 (2003), 347-357.
  14. I. Fazekas,  Z. Rychlik, Almost sure functional limit theorems, Annales  Universitatis Mariae  Curie-Skłodłowska , Lublin – Polonia, Sectio A, Vol. LVI, 1, 2002, 1-18.
  15. E. B. Czerebak-Mrozowicz, O. I. Klesov, Z. Rychlik, Marcinkiewicz-type strong law of large numbers for pairwise independent random fields, Probability and Mathematical Statistics, Vol. 22, Fasc. 1 (2002), pp. 127-139.
  16. I. Gajowiak, Z. Rychlik, Weak convergence of randomly indexed sequences of random variables, Journal of Mathematical Sciences, Vol. 106, No. 1, 2001, 2657-2664.
  17.  Z. Rychlik, T. Walczyński, Convergence in law of random sums with nonrandom centering, Journal of  Mathematical Sciences, Vol. 106, No. 2, 2001, 2860-2864.
  18. O. Klesov, Z. Rychlik, J. Steinebach, Strong limit theorems for general renewal processes, Probability and Mathematical Statistics, Vol. 21, Fasc. 2 (2001), pp. 329-349.
  19. B. Rodzik, Z. Rychlik, Almost sure central limit theorems for weakly dependent random variables, Demonstratio Mathematica, Vol. XXXIV, No. 2, 2001, 365-374. Dedicated to Kazimierz Urbanik on the occasion of his 70th birthday.
  20. Z. Rychlik, T. Walczyński, Convergence in law of random sums with nonrandom centering, Teor. Verojatnost.  i  Primenen., Vol. 46, No. 1, 2001, 188.English translation: Theory of Probability and Its Applications, Vol. 46, 2002, 176-177.
  21. I. Gajowiak, Z. Rychlik, Weak convergence of randomly indexed sequences of random variables, Teor. Verojatnost. i  Primenen., Vol. 45, No. 4, 2000, 804-806. English translation: Theory of Probability and Its Applications, Vol. 45, 2001, 706-707.
  22. O. I. Klesov, Z. Rychlik, Usilennyj zakon bolszich cziseł na czasticzno uporadocznych mnożestwach (in Russian), Teor. Imovirnosti i Matematiczeskaja Statistika, No. 58, 1998, pp. 31 - 37. English translation: Strong law of large numbers on partially ordered sets, Theor.  Probability and Math.  Statist, 58, 1999, 35-41.
  23. P. Kowalski, Z. Rychlik, Limit Theorems for Maximal Random Sums, Asymptotic Methods in Probability and Statistics, A Volume in Honour of Miklos Csorgo, Edited by Barbara Szyszkowicz, 1998 Elsevier Science B. V., Amsterdam-Laussanne-New York-Oxford-Shannon-Singapore-Tokyo, pp. 13 -29.
  24. P. Kowalski,  Z. Rychlik, On the weak law of large numbers for randomly indexed partial arrays, Annales Universitatis Mariae Curie-Skłodowska, Lublin-Polonia, Sectio A, Vol. LI.1, 11(1997), pp. 109-119.
  25. B. Rodzik, Z. Rychlik, On the central limit theorem for independent random variables with almost sure convergence, Probability and Mathematical Statistics, Vol. 16, Fasc. 2(1996), pp.299-309.
  26. P. Kowalski, Z. Rychlik, On the products of a random number of independent random variables, Bull. Polish  Acad. Sci., Math., Vol. 43, No. 3, 1995, 219 230.
  27. A. Łagodowski, Z. Rychlik, Rates of convergence in the weak law for martingale random fields, Proceedings of the Second Ukrainian-Hungarian Conference, M. Arato and M. I. Yadrenko (Eds.), 1995, VSP/TBiMC, 119 - 130.
  28. B. Rodzik, Z. Rychlik, An almost sure central limit theorem for independent random variables, Ann. Inst. Henri Poincare, Vol. 30, No. l, 1994, 1-11, Probabilites et Statistiques.
  29. A. Krajka, Z. Rychlik, Necessary and sufficient conditions for weak convergence of random sums of independent random variables, Comment. Math. Univ. Carolinae, 34, 3(1993), 465 -482.
  30. A. Krajka, Z. Rychlik, The rate of convergence of sums of independent random variables to a stable law, Probability and Mathematical Statistics, Vol. 14, Fasc. 1(1993), pp. 63 - 75.
  31. Z. Rychlik, J. Zygo, Strassen's invariance principle for random subsequences, Statistics & Probability Letters, 13(1992), 193 - 197.
  32. A. Krajka, Z. Rychlik, The rate of convergence of randomly indexed sums of independent random variables to a stable law, Annales  Universitatis  Mariae  Curie-Skłodowska , Lublin-Polonia, Vol. XLVI, 6(1992), Sectio A, 43 - 56.
  33. A. Krajka, Z. Rychlik, On weak and moments convergence of randomly indexed sums, Mathematische  Nachrichten, 157(1992), 249 - 261.
  34. Z. Rychlik, J. Zygo, Almost sure convergence of sequences with random indices, Yokohama Mathematical Journal, Vol. 38(1991), 95 - 101.
  35. P. Matuła,  Z. Rychlik, Distribution and moment convergence of sums of associated random variables, Mathematica  Pannonica, 1/2(1990), 117 - 123.
  36. A. Krajka,  Z. Rychlik, On the rate of convergence in the random central limit theorem in Hilbert space, Probability and Mathematical Statistics, Vol. 11, Fasc. 1(1990), 97 - 108.
  37. P. Matuła, Z. Rychlik, The invariance principle for nonstationary sequences of associated random variables, Ann. Inst. Henri Poincare, Vol. 26, No. 3, 1990, 387 - 397.
  38. Z. A. Łagodowski, Z. Rychlik, Weak convergence of sequences of random elements with multidimensional random indices, Publications  Mathematicae (Debrecen),37(1990), Fasc.1-2,35-40.
  39. A. Krajka,  Z. Rychlik, The order of approximation in the invariance principle for H-valued random sums, Sankhya, The Indian Journal of Statistics, 51(1989), Series A, Pt: 3, 295 -308.
  40. L. E. Gruszecki, Z. Rychlik, Inequalities for conditioned normal approximations, Demonstratio Mathematica, 21(1988), No. 2, 431-440.
  41. A. Krajka, Z. Rychlik, On the limit behaviour of randomly indexed sums of independent random variables, Lit. Mat. Sb., 28(1988), No. 3, 384-494.
  42. M. Polak,  Z. Rychlik, Nonuniform central limit bounds and their applications, Colloquium Mathematicum, Vol. LIV(1988), Fasc.1, 149 158.
  43. A. Krajka,  Z. Rychlik, The order of approximation in the central limit theorem for random summation, Acta  Math. Acad.  Sci. Hung., 51 (1-2)(1988), 109-115.
  44. Z. Rychlik, I. Szyszkowski, The invariance principle for phi-mixing sequences, Teor. Verojatnost.  i   Primenen., 32(1987), No. 3, 616-619. English translation: Theory Probab. Appl., 32(1987), 559-562.
  45. A. Krajka, Z. Rychlik, On the difference between the distribution functions of two random sums of independent random variables, Mathematische  Nachrichten, 134(1987), 317-322.
  46. Z. Rychlik, l. Szyszkowski, Weak convergence of integral type functionals, VNU Science Press BV, "IVth Yilnius Conference on Probability Theory and Mathematical Statistics", 2(1987), 525-534.
  47. Z. Rychlik, I. Szyszkowski, A weak convergence theorem for functionals of sums of martingale differences, Math.  Nachr., 130(1987), 151-155.
  48. L. Paditz,  Z. Rychlik, A note on the Katz-Petrov theorem for random sums, Bull. Polish Acad. Sci., Mat., 34(1986), No. 11-12, 723-727.
  49. A. Krajka,  Z. Rychlik, Approximation of the distribution function of sums of a random number of random variables, Bull. Polish Acad. Sci., Math., Vol. 34, 1986, No. 9-10, 625-634.
  50. Z. A. Łagodowski,  Z. Rychlik, Weak convergence of probability measures on the function space D[0, oo), Bull. Polish  Acad. Sci., Math., 34(1986), No. 5-6, 229-335.
  51. Z. A. Łagodowski,  Z. Rychlik, Convergence rates in the strong law of large numbers for sums of random variables with multidimensional indices, Probability and Mathematical Statistics, 7(1986), Fasc. 2, 149-158.
  52. Z. A. Łagodowski,  Z. Rychlik, Rate of convergence in the strong law of large numbers for martingales, Probability Theory and Related Fields, 71(1976), 467-476.
  53. S. Csorgo,  Z. Rychlik, Rate of convergence in the strong law of large numbers, Probability and Mathematical Statistics, 5(1985), Fasc. 1, 99-111.
  54. Z. Rychlik, Some remarks on stable sequences of random variables, Banach  Center Publications, 16(1985), 455-463.
  55. Z. Rychlik, I. Szyszkowski, The rate of convergence for linear functionals of sums of martingale differences, Proc. of the 4th Pannonian  Symp. on Math. Stat., Bad Tatzmannsdorf,  Austria 1983, Edit. Hungary 1985, 301-310.
  56. Z. Rychlik, I. Szyszkowski, Weak convergence theorem for functionals of sums of reversed martingale arrays, Yokohama Mathematical Journal, 33(1985), 21-28.
  57. A. Krajka,  Z. Rychlik, Weak convergence of random reversed martingales with o-rates, Bull. Polish  Acad. Sci., Math. 33(1985), No. 1-2, 6571.
  58. Z. Rychlik, A remainder term estimate in a random-sum central limit theorem, Bull. Polish  Acad.  Sci.,  Math., 33(1985), No. 1-2, 57-63.
  59. Z. A. Łagodowski, Z. Rychlik, Complete convergence and convergence rates for randomly indexed sums of random variables with multidimensional indices, Bull. Polish  Acad.  Sci.,  Math., 33(1985), No. 3-4, 219-223.
  60. Z. Rychlik, I. Szyszkowski, On the rate of convergence for distributions of  integral type  functionals, Lecture  Notes in Mathematics, 1080(1984), 255-275.
  61. Z. A. Łagodowski, Z. Rychlik, Some remarks on the strong law of large numbers for random fields, Bull. Polish  Acad.  Sci., Math., 32(1984), No. 1-2, 129-134.
  62. Z. Rychlik, I. Szyszkowski, Weak convergence of functionals of sums for martingale differences, Bulletin of the Polish Academy of Sciences, Mathematics, 31(1983), No. 9-12, 407-413.
  63. Z. Rychlik, Nonuniform central limit bounds with applications to probabilities of deviations, Teor. Verojatn. i Primenen,. 28(1983), 646 652.  English  translation: Theory of Probability 28(1983), No. 4, 681 687.
  64. E. Rychlik, Z. Rychlik, On the rates of convergence in the generalized Anscombe theorem, Lit. Mat. Sb., 23(1983), No. 3, 127-133.
  65. Z. Rychlik, On the inequality of Berry-Esseen for the sum of a random number of independent random variables, Matem.  Zametki, 28(1980), 301-304  (in Russian). English  translation:  Math. Notes, 29(1980), 616-617.
  66. M. Csorgo,  Z. Rychlik, Asymptotic properties of randomly indexed sequences of random variables, Canad.  J.  Statistic. 9(1981), 101-107.
  67. M. Csorgo,  Z. Rychlik, On random limit and moderate deviation theorems, Carleton Mathematical Lecture Note, No. 23, 1979.
  68. E. Rychlik, Z. Rychlik, The generalized Anscombe condition and its applications in random limit theorems, Lecture Notes in Mathematics, 828(1980), 244-250.
  69. M. Csorgo,  Z. Rychlik, Weak convergence of sequences of random elements with random indices, Math. Proc.  Camb.  Phil. Soc., 88(1980), 171-174.
  70. Z. Rychlik, Martingale central limit theorem, Acta  Math.  Acad. Sci. Hung., 34(1979),  No. 1-2, 129-139.
  71. Z. Rychlik, The rate of convergence in the certain limit theorems with random indices, lzv.  Akad.  Nauk. Uz.SSR Ser. Fiz. - Mat.  Nauk,  23(1979), 25-29 (in Russian).
  72. Z. Rychlik, D. Szynal, On the rate of approximation in the random-sum central limit theorem, Teor.  Verojatn. i  Primenen.,  24(1979), No. 3, 614-620.
  73. Z. Rychlik, D. Szynal, On the rate of convergence in the central limit theorem, Probability Theory, Banach  Center  Publications,  5(1979), 221-229.
  74. Z. Rychlik, A central limit theorem for martingales, Lit.  Mat.  Sb.,  28(1978),  No. 4, 139-145.
  75. Z. Rychlik, The order of approximation in the random central limit theorem,  Lecture Notes  in  Mathematics,  656(1978), 225-236.
  76. Z. Rychlik, D. Szynal, Inflated truncated negative binomial acceptance sampling plan, Aplikace   Matematiky,  22(1977), No. 3, 157-165.
  77. Z. Rychlik, On the rate of convergence in the random-sum central limit theorem,  Lit. Mat. Sb., 17(1977), 171-178.
  78. Z. Rychlik, A central limit theorem for the sums of a random number of independent random variables, Colloquium  Mathematicum,  35(1976), Fasc. 1, 147-158.
  79. Z. Rychlik, D. Szynal, A functional random-sum central limit theorem ,  Bull. Acad. Polon,  des Sciences, Ser. Math.,  Astr.  et Phys., 23(1975), No. 9, 1013-1018.
  80. Z. Rychlik, D. Szynal, Convergence rates in the central limit theorem for sums of a random number of independent random variables, Teor.  Verojatn. i  Primenen., 20(1975), 359-370.
  81. Z. Rychlik, The convergence of Rosen's series for the sums of a random number of independent random variables, Annales  Universitatis  Mariae  Curie-Skłodowska, Lublin-Polonia, Vol. 28,  Sectio A, No. 8, 1974, 71-83.
  82. Z. Rychlik, D. Szynal, On the convergence rates in the central limit theorem for the sums of a random number of independent identically distributed random variables, Buli.  Acad.  Polon. des Sciences, Ser. Math.,  Astr. et Phys.,  Vol 22, No. 7, 1974, 683-690.
  83. Z. Rychlik, D. Szynal, On the limit behaviour of sums of a random number of independent random variables, Colloquium  Matematicum, Vol. 28, Fasc. 1, 1975, 147 159.
  84. Z. Rychlik, On some inequalities for the concentration function of the sum of a random number of independent random variables, Buli.  Acad.  Polon,  des Sciences, Ser. Math.,  Astr.  et Phys., Vol. 22, No. 1, 1974, 65 70.
  85. Z. Rychlik, D. Szynal, On the limit behaviour of sums of a random number of independent random variables, Buli.  Acad.  Polon, des Sciences, Ser. Math.,  Astr. et Phys., Vol. 20, no. 5, 1972, 401 406.
  86. Z. Rychlik, On some problems concerning of the inflated binomial distribution, Annales  Universitatis  Mariae  Curie-Skłodowska  University, Lublin-Polonia, Vol. 26,  Sectio A, 4, 1972, 38 61.
  87. Z. Rychlik, Rozprawa habilitacyjna : "Rozkłady graniczne losowo indeksowanych ciągów zmiennych losowych", Uniwersytet Marii Curie-Skłodowskiej, Lublin 1980.
  88. Z. Rychlik, Rozprawa doktorska: "Graniczne własności sum niezależnych zmiennych losowych z losową liczbą składników", Uniwersytet Marii Curie-Skłodowskiej, Lublin 1974. Promotor : Doc. dr hab. Dominik Szynal.