Total variation asymptotics for sums of independent integer random variables
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Publication:1872269
DOI10.1214/aop/1023481001zbMath1018.60049OpenAlexW2057712420MaRDI QIDQ1872269
Vydas Čekanavičius, Andrew David Barbour
Publication date: 6 May 2003
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1023481001
Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)
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Cites Work
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- Precision of approximation of the generalized binomial distribution by convolutions of Poisson measures
- Compound Poisson approximation for nonnegative random variables via Stein's method
- Poisson approximations for sequences of random variables
- Compound Poisson approximation in total variation
- Signed Poisson approximations for Markov chains
- On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
- On the Approximation of Polynomial Distributions by Infinitely Divisible Laws
- On Uniform Approximation of the Binomial Distribution by Infinitely Divisible Laws
- On the Convergence Rate in Kolmogorov’s Uniform Limit Theorem. II
- Poisson perturbations
- Asymptotic Expansions in the Exponent: a Compound Poisson Approach
- On improvements of the order of approximation in the Poisson limit theorem
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