Approximation of Symmetric Three-State Markov Chain by Compound Poisson Law

Abstract

The sum of symmetric three-point Markov dependent random variables is approximated by compound Poisson distribution. It is proved that the accuracy of approximation is the same as in compound Poisson approximation to the sum of independent symmetrized Bernoulli variables. Second-order approximations are constructed. The upper-bound and lower-bound estimates are obtained for the total variation, Wasserstein, and local norms.