In memoriam : Czesław Ryll-Nardzewski's contributions to probability theory

• Autorzy: Rolski T. , Woyczyński W. A.

Identyfikatory

DOI

10.19195/0208-4147.37.1.1

• Języki publikacji: EN

Abstrakty

EN

In this paper we review contributions of late Czesław Ryll-Nardzewski to probability theory. In particular, we discuss his papers on point processes, random power series, random series in infinite-dimensional spaces, ergodic theory, de Finetti’s exchangeable sequences, conditional distributions and applications of the Kuratowski-Ryll-Nardzewski theorem on selectors.

Słowa kluczowe

EN

Ryll-Nardzewski; biography; probability theory

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2017
• Tom: Vol. 37, Fasc. 1
• Strony: 1--20
• Opis fizyczny: Bibliogr. 57 poz., fot.

Twórcy

autor

Rolski T.

• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Woyczyński W. A.

• Department of Mathematics, Applied Mathematics and Statistics, Center for Stochastic and Chaotic Processes in Sciences and Technology, Case Western Reserve University, Cleveland, OH 44106

Bibliografia

• [1] J. Mikusiński and C. Ryll-Nardzewski, Sur le produit de composition, Studia Math. 12 (1951), pp. 51-57.
• [2] C. Ryll-Nardzewski, On the ergodic theorems. I (Generalized ergodic theorems), Studia Math. 12 (1951), pp. 65-73.
• [3] C. Ryll-Nardzewski, On the ergodic theorems. II (Ergodic theory of continued fractions), Studia Math. 12 (1951), pp. 74-79.
• [4] C. Ryll-Nardzewski and H. Steinhaus, Sur les fonctions indépendantes. IX (Séries des fonctions positives), Studia Math. 12 (1951), pp. 102-107.
• [5] C. Ryll-Nardzewski, Sur les suites et les fonctions également réparties, Studia Math. 12 (1951), pp. 143-144.
• [6] C. Ryll-Nardzewski and H. Steinhaus, Sur les séries de Taylor, Studia Math. 12 (1951), pp. 159-165.
• [7] J. Mikusiński and C. Ryll-Nardzewski, Sur l’opérateur de translation, Studia Math. 12 (1951), pp. 205-207.
• [8] C. Ryll-Nardzewski, Certaines théorèmes des moments, Studia Math. 12 (1951), pp. 225-226.
• [9] S. Hartman, E. Marczewski, and C. Ryll-Nardzewski, Théorèmes ergodiques et leurs applications, Colloq. Math. 2 (1951), pp. 109-123.
• [10] C. Ryll-Nardzewski, D. Blackwell’s conjecture on power series with random coefficients, Studia Math. 13 (1953), pp. 30-36.
• [11] C. Ryll-Nardzewski, Sur la convergence des séries de puissances de l’opérateur différentiel, Studia Math. 13 (1953), pp. 37-40.
• [12] C. Ryll-Nardzewski, Sur les séries de puissances dans le calcul opératoire, Studia Math. 13 (1953), pp. 41-47.
• [13] J. Mikusiński and C. Ryll-Nardzewski, A theorem on bounded moments, Studia Math. 13 (1953), pp. 51-55.
• [14] J. Mikusiński and C. Ryll-Nardzewski, Un théorème sur le produit de composition des fonctions de plusieurs variables, Studia Math. 13 (1953), pp. 62-68.
• [15] K. Florek, E. Marczewski, and C. Ryll-Nardzewski, Remarks on the Poisson stochastic process. I, Studia Math. 13 (1953), pp. 122-129.
• [16] S. Hartman and C. Ryll-Nardzewski, Théorèmes abstraits de Kronecker et les fonctions presque périodiques, Studia Math. 13 (1953), pp. 296-311.
• [17] C. Ryll-Nardzewski, On the non-homogeneous Poisson process. I, Studia Math. 14 (1954), pp. 124-128.
• [18] C. Ryll-Nardzewski, Remarks on the Poisson stochastic process. III (On a property of the homogeneous Poisson process), Studia Math. 14 (1954), pp. 314-318.
• [19] C. Ryll-Nardzewski, On stationary sequences of random variables and the de Finetti’s equivalence, Colloq. Math. 4 (1957), pp. 149-156.
• [20] C. Ryll-Nardzewski, Remarks on processes of calls, in: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume 2: Contributions to Probability Theory, Univ. California Press, Berkeley, CA, 1961, pp. 455-465.
• [21] D. Blackwell and C. Ryll-Nardzewski, Non-existence of everywhere proper conditional distributions, Ann. Math. Statist. 34 (1963), pp. 223-225.
• [22] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), pp. 397-403.
• [23] K. Musiał, C. Ryll-Nardzewski, and W. A. Woyczyński, Convergence presque sûre des séries aléatoires vectorielles à multiplicateurs bornés, C. R. Acad. Sci. Paris Sér. A 279 (1974), pp. 225-228.
• [24] C. Ryll-Nardzewski and W. A. Woyczyński, Convergence en mesure des séries aléatoires vectorielles à multiplicateur borné, in: Séminaire Maurey-Schwartz (1973-1974): Espaces Lp, applications radonifiantes et géométrie des espaces de Banach. Annexe, Centre de mathématiques, École polytechnique, Paris 1974.
• [25] C. Ryll-Nardzewski and W. A. Woyczyński, Bounded multiplier convergence in measure of random vector series, Proc. Amer. Math. Soc. 53 (1975), pp. 96-98.
• [26] J. Rosiński and C. Ryll-Nardzewski, Cylindrical measures on topological groups, Probab. Math. Statist. 6 (1985), pp. 167-172.
• [27] T. Rolski and C. Ryll-Nardzewski, Is the dying individual the oldest?, Stochastic Process. Appl. 24 (1987), pp. 133-142.
• [28] F. Baccelli and B. Błaszczyszyn, Stochastic Geometry and Wireless Networks. Volume I: Theory, Foundation and Trends in Networking, vol. 3, no. 3-4, Now Publishers, 2009.
• [29] P. Biler, P. Krupski, G. Plebanek, and W. A. Woyczyński, Lwów of the West: A brief history of Wrocław’s New Scottish Book, in: The Scottish Book: Mathematics from the Scottish Café, R. Mauldin (Ed.), second edition, Springer-Birkhäuser 2016, pp. 291-296.
• [30] P. Billingsley, Ergodic Theory and Information, Wiley, New York-London-Sydney 1965.
• [31] É. Borel, Sur les séries de Taylor, C. R. Acad. Sci. Paris 123 (1896), pp. 1051-1052.
• [32] L. Breiman, Probability, Addison-Wesley, Reading, MA, 1968.
• [33] H. Cramér, A contribution to the theory of stochastic processes, in: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Univ. California Press, Berkeley, CA, 1951, pp. 329-340.
• [34] D. J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes, Volume I: Elementary Theory and Methods, Springer, 2003.
• [35] J. Diestel and J. J . Uhl, Jr., Vector Measures, AMS, Providence, R.I., 1977.
• [36] D. Durrett, Probability: Theory and Examples, fourth edition, Cambridge Univ. Press, 2010.
• [37] W. Feller, An Introduction to Probability Theory and Its Applications, vol. 2, second edition, Wiley, New York 1971.
• [38] K. Hinderer, U. Riedel, and M. Stieglitz, Dynamic Optimization: Deterministic and Stochastic Models, Springer, 2016.
• [39] T. C. Hu, E. Nam, A. Rosalsky, and A. I. Volodin, An application of the Ryll-Nardzewski-Woyczyński theorem to a uniform weak law for tail series of weighted sums of random elements in Banach spaces, Statist. Probab. Lett. 48 (2000), pp. 369-374.
• [40] J.-P. Kahane, Sur les fonctions sommes de séries trigonométriques absolument convergentes, C. R. Acad. Sci. Paris 240 (1955), pp. 36-37.
• [41] J.-P. Kahane, Some Random Series of Functions, Heath and Co, 1968.
• [42] O. Kallenberg, Random Measures, Akademie-Verlag-Academic Press, Berlin 1983.
• [43] O. Kallenberg, Foundations of Modern Probability, Springer, 2002.
• [44] A. Ya. Khinchin, Mathematical Methods of the Theory of Mass Service, Tr. Mat. Inst. Steklova, vol. 49, Moscow 1955.
• [45] A. Ya. Khinchin, Flows of random events without after-effects, Teor. Verojatnost. i Primenen. 1 (1956), pp. 3-17.
• [46] J. F. C. Kingman, Completely random measures, Pacific J. Math. 21 (1967), pp. 59-78.
• [47] J. F. C. Kingman, Poisson Processes, Clarendon Press, Oxford 1993.
• [48] K. Knopp, Mengentheoretische Behandlung einiger Probleme der diophantischen Approximationen und der transfiniten Wahrscheinlichkeiten, Mathematische Annalen 95 (1926), pp. 409-426.
• [49] U. Krengel, Ergodic Theorems, W. de Gruyter, Berlin-New York 1985.
• [50] S. Kwapień and W. A. Woyczyński, Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser-Boston, 1992.
• [51] M. Loève, Probability Theory: Foundations, Random Sequences, Van Nostrand, New York 1955.
• [52] E. Marczewski, Remarks on the Poisson stochastic process (II), Studia Math. 13 (1953), pp. 130-136.
• [53] A. Prékopa, On secondary processes generated by a random point distribution of Poisson type, Ann. Univ. Sci. Budapest 1 (1958), pp. 153-170.
• [54] A. Rényi, Remarks on the Poisson process, Studia Sci. Math. Hungar. 2 (1967), pp. 119-123.
• [55] T. Rolski, H. Schmidli, V. Schmidt, and J. Teugels, Stochastic Processes for Insurance and Finance, Wiley, Chichester 1999.
• [56] H. Steinhaus, Über dieWahrscheinlichkeit dafür, dass der Konvergenzkreis einer Potenzreihe ihre natürliche Grenze ist, Math. Z. 31 (1930), pp. 408-416.
• [57] D. Szász and W. A. Woyczyński, Poissonian random measures and linear processes with independent pieces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), pp. 475-482.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).