Convolutions of random measures on compact groups

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2 Scopus citations


Let G be a compact group and M1(G) be the convolution semigroup of all Borel probability measures on G with the weak topology. We consider a stationary sequence {μn}n=-∞+∞ of random measures μnn(ω) in M1(G) and the convolutions {Mathematical expression} and {Mathematical expression} We describe the sets Am+(ω) and An+(ω) of all limit points of vm,n(ω) as m→-∞ or n→+∞ and the set A(ω) of its two-sided limit points for typical realizations of {μn(ω)}n=-∞+∞. Using an appropriate random ergodic theorem we study the limit random measures ρn(±)(ω)=limk→∞ αn(±k)(ω).

Original languageEnglish
Pages (from-to)523-538
Number of pages16
JournalJournal of Theoretical Probability
Issue number3
StatePublished - 1 Jul 1995


  • Convolutions of measures
  • compact group
  • stationary process

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Statistics, Probability and Uncertainty


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