Convolutional attractors of stationary sequences of random measures on compact groups

D. S. Mindlin; B. A. Rubshtein

Annales de l'I.H.P. Probabilités et statistiques (1994)

  • Volume: 30, Issue: 2, page 213-233
  • ISSN: 0246-0203

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Mindlin, D. S., and Rubshtein, B. A.. "Convolutional attractors of stationary sequences of random measures on compact groups." Annales de l'I.H.P. Probabilités et statistiques 30.2 (1994): 213-233. <http://eudml.org/doc/77480>.

@article{Mindlin1994,
author = {Mindlin, D. S., Rubshtein, B. A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {ergodic measure-valued process; compact group; convolution semigroup of Borel probability measures; stationary random process},
language = {eng},
number = {2},
pages = {213-233},
publisher = {Gauthier-Villars},
title = {Convolutional attractors of stationary sequences of random measures on compact groups},
url = {http://eudml.org/doc/77480},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Mindlin, D. S.
AU - Rubshtein, B. A.
TI - Convolutional attractors of stationary sequences of random measures on compact groups
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1994
PB - Gauthier-Villars
VL - 30
IS - 2
SP - 213
EP - 233
LA - eng
KW - ergodic measure-valued process; compact group; convolution semigroup of Borel probability measures; stationary random process
UR - http://eudml.org/doc/77480
ER -

References

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  1. [1] I.P. Cornfeld, S.V. Fomin and Ya G. Sinai, Eegodic Theory, Springer-Verlag, New York, 1981. 
  2. [2] I. Csiszar, On Infinite Products of Random Elements and Infinite Convolutions of probability Distributions on Locally Compact Groups, Z. Wahr. Geb., Vol. 5, 1966, pp. 279-295. Zbl0144.39504MR205306
  3. [3] P.R. Halmos, A Hilbert Space Problembook, D. Van Nostrand company, INC, Toronto, London, 1967. Zbl0144.38704MR208368
  4. [4] H. Heyer, Probability Measures on Locally Compact Groups, Springer-Verlag, Berlin, New York, 1977. Zbl0376.60002MR501241
  5. [5] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Vol. I,II, Springer-Verlag, Berlin, 1963. Zbl0115.10603MR551496
  6. [6] Y. Kawada and K. Itô, On the Probability Distributions on a Compact Group. 1, Proc. Phys.-Math. Soc. Jap., Vol. 22, 1940, pp. 977-998. Zbl0026.13801MR3462JFM66.0544.04
  7. [7] B.M. Kloss, Limit Distributions for Sums of Independent Random Variables Taking Values in a Bicompact Group, Dokt. Akad. Nauk SSSR, Vol. 109, 1956, pp. 453-455, In Russian. Zbl0072.34503MR83212
  8. [8] B.M. Kloss, Probability Distributions on Bicompact Topological Groups, Theor. Prob. Appl., Vol. 6, 1959, pp. 237-270. Zbl0102.14102MR123348
  9. [9] K. Kuratovski, Topology. vv. I, II, Academic Press, New York-London, 1966. Zbl0158.40802MR193605
  10. [10] A. Mukherjea and N.A. Tserpes, Measures on Topological Semigroups, Lec. Notes in Math., Vol. 547, Springer-Verlag, Berlin, New York, 1976. Zbl0342.43001MR467871
  11. [11] V.M. Maksimov, Compositions Sequences of Measures on Compact Groups, Theory Probab. Appl., Vol. 16, 1971, pp. 54-73. Zbl0253.43001MR288799
  12. [12] D.S. Mindlin and B.A. Rubshtein, Convolutions of Random Measures on Compact Groups, Theory Prob. Appl., Vol. 33, 1988, pp. 355-357. Zbl0666.60010MR954587
  13. [13] D.S. Mindlin and B.A. Rubshtein, Random Measures on Compact Groups, Izv Uzb. Acad., VINITI report 3, Vol. 28, 1986, N° 13/192-D. Zbl0808.60012
  14. [14] I.Z. Ruzsa, Infinite Convolutions via Representations, Lect. Notes in Math., Vol. 1064, Springer-Verlag, Berlin-New York, 1988, pp. 398-408. Zbl0542.60015MR772421
  15. [15] V.V. Sazonov and V.N. Tutubalin, Probability Distributions on Topological Groups, Theory Probab. Appl., Vol. 11, 1966, pp. 1-46. Zbl0171.38701MR199872
  16. [16] K. Urbanik, On the Limiting Probability Distributions on a Compact Topological Group, Fund. Math., Vol. 44, 1957, pp. 253-261. Zbl0203.49902MR92921

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