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- W2072097185 abstract "Let $(X_n: n geqq 1)$ be a sequence of independent random variables, each having mean 0 and a finite variance. Under the Lindeberg condition and uniformity conditions on the characteristic functions, it is shown that the local limit theorem holds, i.e., if $S_n$ is the $n$th partial sum of the sequence, then $(2pi operatorname{Var} S_n)^{frac{1}{2}}P(S_n in (a, b)) rightarrow b - a$. Under the assumption that the local limit theorem holds for each tail of $(X_n)$, and one other condition, it is then shown that the random walk generated by $(X_n)$ is recurrent if $sum (operatorname{Var} S_n)^{-frac{1}{2}} = infty$." @default.
- W2072097185 created "2016-06-24" @default.
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- W2072097185 date "1978-08-01" @default.
- W2072097185 modified "2023-09-25" @default.
- W2072097185 title "On the Local Limit Theorem for Independent Nonlattice Random Variables" @default.
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- W2072097185 doi "https://doi.org/10.1214/aop/1176995478" @default.
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