PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1995 | 61 | 1 | 25-38
Tytuł artykułu

On concentrated probabilities

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence $g_n ∈ G$ such that $μ^{∗n}(g_n A) ≡ 1$ for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power $μ^{∗k}$ has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological group G.
Twórcy
  • Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, P.O. Box 392 0001 Pretoria, South Africa
Bibliografia
  • [B1] W. Bartoszek, On the asymptotic behaviour of iterates of positive linear operators, Notices South African Math. Soc. 25 (1993), 48-78.
  • [B2] W. Bartoszek, On concentration functions on discrete groups, Ann. Probab., to appear.
  • [B3] W. Bartoszek, On the equation μ̌ ∗ϱ∗μ = ϱ, Demonstratio Math., to appear.
  • [C] I. Csiszár, On infinite products of random elements and infinite convolutions of probability distributions on locally compact groups, Z. Wahrsch. Verw. Gebiete 5 (1966), 279-299.
  • [CFS] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, New York, 1981.
  • [DL1] Y. Derriennic et M. Lin, Sur le comportement asymptotique de puissances de convolution d'une probabilité, Ann. Inst. H. Poincaré 20 (1984), 127-132.
  • [DL2] Y. Derriennic et M. Lin, Convergence of iterates of averages of certain operator representations and of convolution powers, J. Funct. Anal. 85 (1989), 86-102.
  • [H] H. Heyer, Probability Measures on Locally Compact Groups, Springer, Berlin, 1977.
  • [HR] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I, Springer, Berlin, 1963.
  • [HM] K. H. Hofmann and A. Mukherjea, Concentration functions and a class of non-compact groups, Math. Ann. 256 (1981), 535-548.
  • [M] A. Mukherjea, Limit theorems for probability measures on non-compact groups and semigroups, Z. Wahrsch. Verw. Gebiete 33 (1976), 273-284.
  • [P] K. R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967.
  • [T] A. Tortrat, Lois de probabilité sur un espace topologique complétement régulier et produits infinis à termes indépendants dans un groupe topologique, Ann. Inst. H. Poincaré Sect. B 1 (1965), 217-237
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv61z1p25bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.