The Kloss convergence principle for products of random variables with values in a compact group and distributions determined by a Markov chain
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I. A. Kruglov
Abstract
In this paper we study the weak convergence of distributions for products of random variables with values in a compact group provided that the distributions of the factors are defined by a finite simple homogeneous irreducible Markov chain. We show that after an appropriate shift the sequence of distributions of these products converges weakly to the normalised Haar measure on some closed subgroup of the initial group, in other words, the convergence principle due to B. M. Kloss holds true, which has been established earlier for products of independent factors. We describe conditions on the Markov chain and on the initial distributions which guarantee that the limit behaviour of the distribution of the products is similar to the limit behaviour of the distributions of some products of independent random variables.
© de Gruyter 2008
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- Random polynomials over a finite field
- Random permutations with cycle lengths in a given finite set
- The Kloss convergence principle for products of random variables with values in a compact group and distributions determined by a Markov chain
- On enumeration of labelled connected graphs by the number of cutpoints
- Skew Laurent series rings and the maximum condition on right annihilators
- A block algorithm of Lanczos type for solving sparse systems of linear equations
- On complexity of the anti-unification problem
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Articles in the same Issue
- Random polynomials over a finite field
- Random permutations with cycle lengths in a given finite set
- The Kloss convergence principle for products of random variables with values in a compact group and distributions determined by a Markov chain
- On enumeration of labelled connected graphs by the number of cutpoints
- Skew Laurent series rings and the maximum condition on right annihilators
- A block algorithm of Lanczos type for solving sparse systems of linear equations
- On complexity of the anti-unification problem
- Classification of indecomposable Abelian (v, 5)-groups
