Mod-discrete expansions

• 成果类型: Article
• 署名作者: Barbour, A. D.; Kowalski, E.; Nikeghbali, A.
• 署名单位: University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0498-8
• 发表日期: 2014
• 页码: 859-893
• 关键词: DISTRIBUTIONS; approximation; asymptotics

摘要

In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in which convergence in law (without normalization) cannot be expected. The setting is one in which the simplest approximation to the -th random variable is by a particular member of a given family of distributions, whose variance increases with . The basic assumption is that the ratio of the characteristic function of to that of converges to a limit in a prescribed fashion. Our results cover and extend a number of classical examples in probability, combinatorics and number theory.