Convergence faible avec indices aléatoires
Fischler, Roger
Annales de l'I.H.P. Probabilités et statistiques, Tome 12 (1976), p. 391-399 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1976-01-01
@article{AIHPB_1976__12_4_391_0,
     author = {Fischler, Roger},
     title = {Convergence faible avec indices al\'eatoires},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {12},
     year = {1976},
     pages = {391-399},
     mrnumber = {431345},
     zbl = {0362.60023},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPB_1976__12_4_391_0}
}

Fischler, Roger. Convergence faible avec indices aléatoires. Annales de l'I.H.P. Probabilités et statistiques, Tome 12 (1976) pp. 391-399. http://gdmltest.u-ga.fr/item/AIHPB_1976__12_4_391_0/

[1] F.J. Anscombe, Large-sample theory of sequential estimation. Proc. Cambridge Philos. Soc., t. 48, 1952, p. 600-607. | MR 51486 | Zbl 0047.13401

[2] P. Billingsley, Limit theorems for randomly selected partiel sums. Ann. Math. Stat., t. 33, 1962, p. 85-92. | MR 137138 | Zbl 0113.12402

[3] P. Billingsley, Convergence of Probability Measures. Wiley, 1968. | MR 233396 | Zbl 0172.21201

[4] M. Csörgö, R. Fischler and P. Revesz, Random limit theorems via strong invariance principles. Carleton University, Mathematics Department, Publication.

[5] M. Csörgö and R. Fischler, Departure from Independence, the strong law, standard and random-sum central limit theorems. Acta Math. Acad. Sci. Hung., t. 21, 1970, p. 105-114. | MR 266277 | Zbl 0221.60016

[6] M. Csörgö and R. Fischler, On mixing and the central limit theorem. Tohoku Math. J., t. 23, 1971, p. 139-145. | MR 290429 | Zbl 0237.60013

[7] M. Csörgö and S. Csorgo, On weak convergence of randomly selected partiel sums. Acta Sci. Math. Segediensis, t. 34, 1973, p. 53-60. | MR 321157 | Zbl 0267.60024

[8] M. Csörgö and R. Fischler, Some examples and results in the theory of mixing and random-sum central limit theorems. Periodica Mathematica Hungarica, t. 3, 1973, p. 41-57. | MR 331474 | Zbl 0269.60017

[9] W. Döblin, Sur deux problèmes de M. Kolmogoroff concernant les chaînes dénombrables. Bull. Soc. Math. France, t. 66, 1938, p. 210-220. | Numdam | MR 1505091 | Zbl 0020.14604

[10] W. Döblin, Éléments d'une théorie générale des chaînes simples constant de Markov. Ann. Sci. École Normale Sup., t. 57 (3), 1940, p. 61-111. | Numdam | MR 4409 | Zbl 0024.26503

[11] W. Feller, An Introduction to the Theory of Probability and its Applications, Vol. 2, Wiley, 1966. | MR 210154 | Zbl 0138.10207

[12] P. Fernandez, A weak convergence theorem for random sums of independent random variables. Ann. Math. Stat., t. 41, 1970, p. 710-712. | MR 254906 | Zbl 0201.20403

[13] R. Fischler, Decomposition and composition of mixing sequences. J. Math. Anal. and App., t. 21, 1968, p. 389-395. | MR 221546 | Zbl 0239.60040

[14] R. Fischler, Suites de bi-probabilités stables. Annales de la Faculté des Sciences de l'Université de Clermont, n° 43, 1970, p. 159-167. | Numdam | MR 293694 | Zbl 0233.60029

[15] R. Fischler, Stable sequences of random variables and the weak convergence of the associated empirical measures. Sankhya, Series A, t. 33, 1971, p. 67-72. | MR 303572 | Zbl 0233.60028

[16] R. Fischler, Quelques théorèmes limites du calcul des probabilités dont la valeur limite dépend d'une variable aléatoire. Ann. Inst. Henri Poincaré (B), t. 9, 1973, p. 345-349. | Numdam | MR 341569 | Zbl 0276.60040

[17] D. Friedman, Brownian Motion and Diffusion. Holden-Day, 1971. | Zbl 0231.60072

[18] S. Guiasu, Asymptotic distribution for stochastic processes with random discrete time. Trans. 4th Prague Conf. on Information Theory, Statistical Decision Functions, Random Processes, Publishing House of the Czech. Acad. Sci., 1967, p. 307-321. | MR 217855

[19] S. Guiasu, Contributii la studiul reportitiei limita a proceselor stocastice au timp discret aleator. Studii Si Cercetari Matematice.

[20] S. Guiasu, On the asymptotic distribution of the sequences of randcm variables with random indices. Ann. Math. Stat., t. 42, 1971, p. 2018-2028. | MR 307427 | Zbl 0229.60026

[21] J. Lamperti, On extreme order statistics. Ann. Math. Stat., t. 35, 1964, p. 1726-1737. | MR 170371 | Zbl 0132.39502

[22] D. Mccleish, Dependent central limit theorems and invariance principles. Ph. D. Thesis, McGill University, 1972.

[23] J. Mogyoródi, On limiting distributions for sums of a random number of independent random variables. Publications of the Math. Inst. Hung. Acad. Sci., t. 6 A, 1961, p. 365-371. | MR 148098 | Zbl 0106.12504

[24] J. Mogyoródi, Limit distributions for sequences of random variables with random indices. Trans. 4th Prague Conf. on Information Theory, Statistical Decision Functions, Random Processes, Prague, 1967, p. 463-470. | MR 217846

[25] J. Mogyoródi, A remark on stable sequences of random variables and a limit distribution theorem for a random sum of independent random variables. Acta Math. Acad. Sci. Hung., t. 17, 1966, p. 401-409. | MR 202177 | Zbl 0203.19603

[26] A. Rényi, On stable sequences of events. Sankyha, t. 25 A, 1963, p. 293-302. | MR 170385 | Zbl 0141.16401

[27] A. Rényi, Foundations of Probability. Holden-Day, 1970. | MR 264723 | Zbl 0203.49801

[28] S. Resnick, Weak convergence to extremal processes. Stanford University, Dept of Statistics, Technical Report n° 49, 1973.

[29] W. Richter, Ein zentraler Grenzwertsats für das Maximum einer zufalligen Anzahle unabhängiger Zufallsgrossen. Wissenschaftliche Zeitschrift der Technischen Universität Dresden, t. 13, 1964, Heft 5, p. 1343-1346. | MR 183007 | Zbl 0192.25301

[30] W. Richter, Limit theorems for sequences of random variables with sequences of random indices. Theory of Prob. and App., t. 10, 1965, p. 74-84. | Zbl 0139.35204

[31] W. Richter, Übertragung von Grenzaussagen für folgen zufalliger Elemente auf Folgen mit zufalligen Indizes. Math. Nachrichten, t. 29, 1965, p. 347-365. | MR 190981 | Zbl 0143.20703

[32] W. Richter, Das null-ein Gesetzt und ein Grenzwertsats für zufallige Elemente mit diskreter zufalliger Zeit. Wissenschaftliche Zeitschrift der Technischen Universität Dresden, t. 14, 1965, Heft 3, p. 497-504. | MR 203782 | Zbl 0203.19404

[33] R. Salem and A. Zygmund, On lacunary trigonometric series I. Proc. Nat. Acad. Sci. U. S. A., t. 33, 1947, p. 333-338. | MR 22263 | Zbl 0029.11902

[34] J.C. Smith, On the asymptotic distribution of the sums of Rademacher functions. Bull. Amer. Math. Soc., t. 51, 1945, p. 941-944. | MR 13848 | Zbl 0063.07089

[35] M. Sreehari, An invariance principle for random partial sums. Sankyha, t. 30 A, 1968, p. 433-442. | Zbl 0292.60042

[36] L. Sucheston, On mixing and the 0 - 1 law. J. Math. App. Anal., t. 6, 1963, p. 447-456. | MR 149524 | Zbl 0118.13504

[37] D. Szasz, Limit theorems for the distributions of the sums of a random number of random variables. A paraître.

[38] S. Takahashi, On the central limit theorem. Tohoku Math. J., t. 3, 1951, p. 316-321. | MR 47278 | Zbl 0044.33603

[39] S. Takahashi, On the asymptotic distribution of the sum of independent random variables. Proc. Japan Acad., t. 27, 1951, p. 393-400. | MR 47959 | Zbl 0045.07503