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Probability Surveys, 2019 We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict ourselves to a particular method, and overview the whole range of issues including the general limit theorem, estimates
S Y Novak
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Poisson Approximation for Dependent Trials
Annals of Probability, 1975 Let $X_1, \cdots, X_n$ be an arbitrary sequence of dependent Bernoulli random variables with $P(X_i = 1) = 1 - P(X_i = 0) = p_i.$ This paper establishes a general method of obtaining and bounding the error in approximating the distribution of $\sum^n_{i=1} X_i$ by the Poisson distribution.
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On the Poisson Equation and Diffusion Approximation. I [PDF]
Annals of Probability, 2001 The authors consider the Poisson equation \(Lu=-f\) in the entire \(d\)-dimensional space. \(L\) denotes a second-order elliptic differential operator which is the generator of a positive recurrent diffusion process \(X\). The function \(f\) is assumed to be centred with respect to the invariant measure of \(X\).
E Pardoux
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A Semigroup Approach to Poisson Approximation
Annals of Probability, 1986 Let \(X_ 1,...,X_ n\) be independent Bernoulli r.v.'s with \(p_ j=P(X_ j=1)=1-P(X_ j=0 ...
D Pfeifer
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A General Poisson Approximation Theorem
Annals of Probability, 1975 A sum of nonnegative integer-valued random variables may be treated as a Poisson variable if the summands have sufficiently high probabilities of taking 0 value and sufficiently weak mutual dependence. This paper presents simple exact upper bounds for the error of such an approximation.
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Improvements of Poisson approximation for n-dimensional unit cube random graph [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2021 This paper uses the Stein-Chen method to obtain uniform and non-uniform bounds in the Poisson approximation for the n-dimensional unit cube random graph. These bounds are re-established under the restriction of Poisson mean λ = 1.
Kanint Teerapabolarn
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On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law
Mathematics, 2021 A subject of this study is the behavior of the tail of the binomial distribution in the case of the Poisson approximation. The deviation from unit of the ratio of the tail of the binomial distribution and that of the Poisson distribution, multiplied by ...
Sergei Nagaev, Vladimir Chebotarev
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A hooray for Poisson approximation [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We give several examples for Poisson approximation of quantities of interest in the analysis of algorithms: the distribution of node depth in a binary search tree, the distribution of the number of losers in an election algorithm and the discounted ...
Rudolf Grübel
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Condensed Matter Physics, 2021 Structure and thermodynamics in restricted primitive model electrolytes are examined using three recently developed versions of a linear form of the modified Poisson-Boltzmann equation.
L. B. Bhuiyan
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$S$-constrained random matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 Let $S$ be a set of $d$-dimensional row vectors with entries in a $q$-ary alphabet. A matrix $M$ with entries in the same $q$-ary alphabet is $S$-constrained if every set of $d$ columns of $M$ contains as a submatrix a copy of the vectors in $S$, up to ...
Sylvain Gravier, Bernard Ycart
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