| Abstract [eng] |
In this thesis, we apply compound Poisson type approximations to sums of Markov dependent integer-valued random variables. It is shown that in the scheme of sequences the translated Poisson approximation has the same accuracy as the Normal approximation. A partial case of the first uniform Kolmogorov theorem for the Markov binomial distribution is proved. It is proved that the limit law of symmetric three-state Markov chain is a compound Poisson distribution with the compounding geometric distribution and the approximation is of the order O(1/n). Apart from the total variation metric, the Kolmogorov, Wasserstein and local metrics are also used. Second order estimates, non-uniform and lower bound estimates were obtained. It is proved that the Simons-Johnson theorem holds for the Markov binomial distribution and the distribution based on a symmetric three-state Markov chain, that is the convergence to a compound Poisson limit holds with exponential weights. |
