- 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).
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- I. Ćwiklińska, Z. Rychlik, Weak convergence of random sums and maximum random sums under nonrandom norming, Fields Institute Communications, Vol. 44, 2004, 245 – 263.
- 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.
- I. Fazekas, Z. Rychlik, Almost sure central limit theorems for random fields, Math. Nachr. 259, (2003), 12 – 18.
- Z. Rychlik, K. S. Szuster, On strong versions of the central limit theorem, Statistics&Probability Letters, 61 (2003), 347-357.
- I. Fazekas, Z. Rychlik, Almost sure functional limit theorems, Annales Universitatis Mariae Curie-Skłodłowska , Lublin – Polonia, Sectio A, Vol. LVI, 1, 2002, 1-18.
- 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.
- I. Gajowiak, Z. Rychlik, Weak convergence of randomly indexed sequences of random variables, Journal of Mathematical Sciences, Vol. 106, No. 1, 2001, 2657-2664.
- Z. Rychlik, T. Walczyński, Convergence in law of random sums with nonrandom centering, Journal of Mathematical Sciences, Vol. 106, No. 2, 2001, 2860-2864.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Z. Rychlik, J. Zygo, Strassen's invariance principle for random subsequences, Statistics & Probability Letters, 13(1992), 193 - 197.
- 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.
- A. Krajka, Z. Rychlik, On weak and moments convergence of randomly indexed sums, Mathematische Nachrichten, 157(1992), 249 - 261.
- Z. Rychlik, J. Zygo, Almost sure convergence of sequences with random indices, Yokohama Mathematical Journal, Vol. 38(1991), 95 - 101.
- P. Matuła, Z. Rychlik, Distribution and moment convergence of sums of associated random variables, Mathematica Pannonica, 1/2(1990), 117 - 123.
- 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.
- 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.
- 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.
- 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.
- L. E. Gruszecki, Z. Rychlik, Inequalities for conditioned normal approximations, Demonstratio Mathematica, 21(1988), No. 2, 431-440.
- 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.
- M. Polak, Z. Rychlik, Nonuniform central limit bounds and their applications, Colloquium Mathematicum, Vol. LIV(1988), Fasc.1, 149 158.
- 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.
- 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.
- 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.
- 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.
- Z. Rychlik, I. Szyszkowski, A weak convergence theorem for functionals of sums of martingale differences, Math. Nachr., 130(1987), 151-155.
- 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.
- 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.
- 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.
- 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.
- 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.
- S. Csorgo, Z. Rychlik, Rate of convergence in the strong law of large numbers, Probability and Mathematical Statistics, 5(1985), Fasc. 1, 99-111.
- Z. Rychlik, Some remarks on stable sequences of random variables, Banach Center Publications, 16(1985), 455-463.
- 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.
- Z. Rychlik, I. Szyszkowski, Weak convergence theorem for functionals of sums of reversed martingale arrays, Yokohama Mathematical Journal, 33(1985), 21-28.
- A. Krajka, Z. Rychlik, Weak convergence of random reversed martingales with o-rates, Bull. Polish Acad. Sci., Math. 33(1985), No. 1-2, 6571.
- 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.
- 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.
- Z. Rychlik, I. Szyszkowski, On the rate of convergence for distributions of integral type functionals, Lecture Notes in Mathematics, 1080(1984), 255-275.
- 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.
- 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.
- 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.
- E. Rychlik, Z. Rychlik, On the rates of convergence in the generalized Anscombe theorem, Lit. Mat. Sb., 23(1983), No. 3, 127-133.
- 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.
- M. Csorgo, Z. Rychlik, Asymptotic properties of randomly indexed sequences of random variables, Canad. J. Statistic. 9(1981), 101-107.
- M. Csorgo, Z. Rychlik, On random limit and moderate deviation theorems, Carleton Mathematical Lecture Note, No. 23, 1979.
- E. Rychlik, Z. Rychlik, The generalized Anscombe condition and its applications in random limit theorems, Lecture Notes in Mathematics, 828(1980), 244-250.
- M. Csorgo, Z. Rychlik, Weak convergence of sequences of random elements with random indices, Math. Proc. Camb. Phil. Soc., 88(1980), 171-174.
- Z. Rychlik, Martingale central limit theorem, Acta Math. Acad. Sci. Hung., 34(1979), No. 1-2, 129-139.
- 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).
- 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.
- Z. Rychlik, D. Szynal, On the rate of convergence in the central limit theorem, Probability Theory, Banach Center Publications, 5(1979), 221-229.
- Z. Rychlik, A central limit theorem for martingales, Lit. Mat. Sb., 28(1978), No. 4, 139-145.
- Z. Rychlik, The order of approximation in the random central limit theorem, Lecture Notes in Mathematics, 656(1978), 225-236.
- Z. Rychlik, D. Szynal, Inflated truncated negative binomial acceptance sampling plan, Aplikace Matematiky, 22(1977), No. 3, 157-165.
- Z. Rychlik, On the rate of convergence in the random-sum central limit theorem, Lit. Mat. Sb., 17(1977), 171-178.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Z. Rychlik, Rozprawa habilitacyjna : "Rozkłady graniczne losowo indeksowanych ciągów zmiennych losowych", Uniwersytet Marii Curie-Skłodowskiej, Lublin 1980.
- 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.