Limit theorems for sums of identically distributed random variables assuming restricted convergence of their distribution functions | Zendy

Rossberg HansJoachim | Zendy

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Limit theorems for sums of identically distributed random variables assuming restricted convergence of their distribution functions

Author(s) -

Rossberg HansJoachim

Publication year - 1983

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19831130113

Subject(s) - mathematics , independent and identically distributed random variables , lemma (botany) , random variable , convergence of random variables , central limit theorem , infinite divisibility , limit (mathematics) , distribution (mathematics) , convergence (economics) , sum of normally distributed random variables , illustration of the central limit theorem , discrete mathematics , mathematical analysis , statistics , ecology , poaceae , economics , biology , economic growth

Let F n stand for the distribution of a normalized sum of n independent random variables with common distribution H . In [6] we assumed the restricted convergence.and obtain an analogous result. The method of proof is considerably different, in particular a very recent continuation theorem (lemma 3.2) for infinitely divisible distributions is needed.

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