A NOTE ON ASYMPTOTIC EXPANSIONS FOR SUMS OVER A WEAKLY DEPENDENT RANDOM FIELD WITH

APPLICATION TO THE POISSON AND STRAUSS PROCESSES

J. L. JENSEN

Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark

(Received July 1, 1991; revised July 17, 1992)

Abstract. Previous results on Edgeworth expansions for sums over a random field are extended to the case where the strong mixing coefficient depends not only on the distance between two sets of random variables, but also on the size of the two sets. The results are applied to the Poisson and the Strauss point processes, giving rise also to local limit results.

Key words and phrases: Conditional Cramér condition, local limit theorem, Poisson process, Strauss process.