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A note on a strong renewal theorem
Author(s) -
Mohan N. R.
Publication year - 1977
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314780
Subject(s) - mathematics , exponent , independent and identically distributed random variables , sequence (biology) , combinatorics , domain (mathematical analysis) , distribution (mathematics) , function (biology) , random variable , discrete mathematics , mathematical analysis , statistics , philosophy , linguistics , evolutionary biology , biology , genetics
Let { S n , n ≥ 1} be a sequence of partial sums of independent and identically distributed non‐negative random variables with a common distribution function F. Let F belong to the domain of attraction of a stable law with exponent α, 0 < α < 1. Suppose H(t) = ϵ N(t), t ⩾ 0, where N(t) = max(n : S n ≥ t ). Under some additional assumptions on F , the difference between H(t) and its asymptotic value as t → ∞ is estimated.