On multivariate Le Cam theorem and compound Poisson measures (Q1916225)

The distribution of a sum of independent random variables can frequently be well approximated by that of a related compound Poisson distribution; see, for example \textit{L. Le Cam} [in: Proc. Prague Symp. Asympt. Stat., Vol. I, 179-200 (1974; Zbl 0365.62032)] for identically distributed random variables, and \textit{Eh. L. Presman} [Theory Probab. Appl. 18, 378-384 (1973); translation from Teor. Veroyatn. Primen. 18, 396-402 (1973; Zbl 0307.60030)] for the multivariate extensions. Closer approximations are achieved by using members of the larger class of signed compound Poisson measures, again in the context of identically distributed summands. For non-identically distributed summands, the situation is less satisfactory, but some variants of \textit{Hipp's} expansion [ASTIN Bull. 6, 89-100 (1986)] are established.