TY - JOUR
AB - 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.
AU - GĂ¶tze, Friedrich
AU - Heinrich, L
AU - Hipp, C
ID - 1640785
IS - 2
JF - SCANDINAVIAN JOURNAL OF STATISTICS
KW - M-DEPENDENT RANDOM FIELD
KW - KIRKWOOD-SALSBURG EQUATIONS
KW - POISSON CLUSTER PROCESS
KW - BOOLEAN MODEL
KW - CUMULANT GENERATING FUNCTION
SN - 0303-6898
TI - M-DEPENDENT RANDOM-FIELDS WITH ANALYTIC CUMULANT GENERATING FUNCTION
VL - 22
ER -