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A Note on the Local Limit Theorem for Large Deviations
Theory of Probability & Its Applications, 1991An answer to the question whether the Cramér condition is necessary for the local limit theorem for large deviations is given in the following: Let \(\{X_ i\}^ \infty_{i=1}\) be a sequence of i.i.d. r.v.s, \(EX_ 1=0\), \(DX_ 1=1\), \(S_ n={1\over\sqrt n}\sum^ n_{i=1} X_ i\), then \[ p_ n(x)={1\over\sqrt{2\pi}}\exp\left\{-{x^ 2\over 2}+{x^ 3\over\sqrt n}
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On a Local Limit Theorem for Lattice Random Variables
Theory of Probability & Its Applications, 1964Yu. V. Prokhorov made a conjecture that the two statements are equivalent: (a) the local limit theorem is applicable to a sequence of integer-valued random variables, (b) these variables obey the central limit theorem and their sums are asymptotically uniformly distributed modulo h for arbitrary h.We give an example showing that the above conjecture ...
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The Local Limit Theorem in the Reducible Case
2023Dmitry Dolgopyat, Omri M. Sarig
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Local limit theorems for complex functions on
Journal of Mathematical Analysis and Applications, 2023Evan D. Randles
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On a Weak Form of a Local Limit Theorem
Theory of Probability & Its Applications, 1977openaire +1 more source
Local limit theorems in some random models from number theory
Stochastic Analysis and Applications, 2016Rita Giuliano, Michel Weber
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Parabolic Harnack inequality and local limit theorem for percolation clusters
Electronic Journal of Probability, 2009Martin T. Barlow
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