PUB - Publikationen an der Universität Bielefeld

We consider m-dependent random fields of bounded random vectors (generated by independent random fields) and investigate the analyticity of the cumulant generating function of sums of these random vectors. Using the Kirkwood-Salsburg equations we derive upper bounds for the cumulant generating function and prove its analyticity in a neighbourhood of zero, where the normalized bounds and the neighbourhood are independent of the number of terms in the sum, The results are applied to statistics of Poisson cluster processes and Boolean models (which have a representation in terms of an independent field) and yield probabilities of large deviations as well as Berry-Esseen results for these statistics.