不同分布的卷积的局部封闭性及局部渐近性的充分条件和必要条件

THE SUFFICIENT CONDITION AND NECESSARY CONDITION OF LOCAL CLOSURE AND LOCAL ASYMPTOTIC FOR THE CONVOLUTIONS OF NON-IDENTICAL DISTRIBUTIONS

得到了支撑在[0,∞)上的不同分布的卷积(包括卷积根)的局部封闭性及局部渐近性的充分条件和必要条件,它揭示了不同分布的卷积及两两卷积之间的内在关系.这一结果的充分性部分推广了Geluk等非局部的相应结果,并且两者使用的方法是不同的;而这一结果的必要性部分是Geluk等人的结果中所没有的.最后,讨论了(-∞,∞)上不同分布卷积的局部封闭性及局部渐近性.

This paper is concerned with some sufficient conditions and necessary conditions of local closure and local asymptotics for the convolutions （including convolution roots）of non-identical distributions on [0, ∞）, which reveal the relations between convolutions and pairwise convolutions of non-identical distributions. The sufficient part of the result extends the corresponding non-local result of Geluk（2006）, and the methods used here are different from theirs, the necessary part of the result is not included in the Geluk＇s paper. Finally, the local closure and local asymptotics for the convolutions of non-identical distributions on （-∞,∞） are considered.