Limit Theorems for Dense F-Reccurent Series and Chains Numbers in Sequence of Independent Random Variables

The work is devoted to studying properties of distribution of dense F-recurrent series and chains with given length in the sequence of independent identically distributed random variables over finite alphabet. Using functional modification of Chen-Stein method we investigate estimators of convergence rate of distribution of numbers of dense F-recurrent series with given lengths to accompanying multivariate Poisson distribution (in metric of distance by variance). On the ground of this results multivariate Poisson limit theorem and central limit theorem for numbers of dense F -recurrent series with given lengths and length no less than given were derived under appropriate variation of scheme parameters. The estimators of distance by variance also allow to derive conditions under which distribution of dense F-recurrent chains with given length converges to compound Poisson distribution.

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