Compound Poisson approximations in $\ell_p$-norm for sums of weakly dependent vectors

The distribution of the sum of 1-dependent lattice vectors with supports on coordinate axes is approximated by a multivariate compound Poisson distribution and by signed compound Poisson measure. The local and $\ell_α$-norms are used to obtain the error bounds. The Heinrich method is used for the proofs.

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