Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

Versik processes and very weak Bernoulli processes with summable rates are independent


Authors: Herold Dehling, Manfred Denker and Walter Philipp
Journal: Proc. Amer. Math. Soc. 91 (1984), 618-624
MSC: Primary 28D05; Secondary 60G10
DOI: https://doi.org/10.1090/S0002-9939-1984-0746101-0
MathSciNet review: 746101
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that very weak Bernoulli processes and Versik processes having dependence rates $ o(1/n)$ are independent or $ 2$-dependent respectively. The borderline case where the rate is $ O(1/n)$ is discussed in some detail.

References [Enhancements On Off] (What's this?)

  • [I] Berkes and W. Philipp (1979), Approximation theorems for independent and weakly dependent random vectors, Ann. Probab. 7, 29-54. MR 515811 (80k:60008)
  • [R] C. Bradley (1983), On a very weak Bernoulli condition, preprint. MR 752477 (86a:28018)
  • [R] M. Dudley (1976), Probabilties and metrics, Aarhus Univ. Math. Inst. Lecture Notes Ser., No. 45, Aarhus. MR 0488202 (58:7764)
  • [E] Eberlein (1983), Strong approximation of very weak Bernoulli processes, Z. Wahrsch. Verw. Gebiete 62, 17-37. MR 684206 (85c:60039)
  • [R] M. Gray, D. L. Neuhoff and P. C. Shields (1975), A generalisation of Ornstein's $ d$-distance with applications to information theory, Ann. Probab. 3, 315-328. MR 0368127 (51:4369)
  • [D] Ornstein (1974), Ergodic theory, randomness, and dynamical systems, Yale Math. Mono., No. 5, Yale Univ. Press, New Haven. MR 0447525 (56:5836)
  • [J] W. Pitman (1974), Uniform rates of convergence for Markov chain transition probabilities, Z. Wahrsch. Verw. Gebiete 29, 193-227. MR 0373012 (51:9214)
  • [A] Rothstein (1980), Versik processes: First steps, Israel J. Math. 36, 205-223. MR 597450 (82c:28035)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28D05, 60G10

Retrieve articles in all journals with MSC: 28D05, 60G10

Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0746101-0
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society