Almost sure local central limit theorem for the product of some partial sums with optimized weight

Feng Xu, Binhui Wang and Yawen Hou

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 13, 3051-3062

Abstract: The almost sure local central limit theorem is a general result which contains the almost sure global central limit theorem. Let {Xk,k≥1} be a sequence of independent and identically distributed (i.i.d.) positive random variables. Under a fairly general condition an universal result in almost sure local limit theorem for the product of some partial sums (∏i=1kSk,i/((k−1)kμk))1/(γk) is established on the weight dk=k−1 exp ( log βk),0≤β

Date: 2021
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DOI: 10.1080/03610926.2019.1680694

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