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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.
Louis H Y Chen
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On the Poisson equation and diffusion approximation 3
Annals of Probability, 2005 We study the Poisson equation Lu+f=0 in R^d, where L is the infinitesimal generator of a diffusion process. In this paper, we allow the second-order part of the generator L to be degenerate, provided a local condition of Doeblin type is satisfied, so ...
E Pardoux, A Yu Veretennikov
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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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On moderate deviations in Poisson approximation [PDF]
Journal of Applied Probability, 2020 AbstractIn this paper we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of a Poisson distribution than those of the normal distribution.
Qingwei Liu, Aihua Xia
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Relaxation of monotone coupling conditions: Poisson approximation and beyond [PDF]
, 2017 It is well-known that assumptions of monotonicity in size-bias couplings may be used to prove simple, yet powerful, Poisson approximation results. Here we show how these assumptions may be relaxed, establishing explicit Poisson approximation bounds ...
Daly, Fraser, Johnson, Oliver
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The Annals of Applied Probability, 2009 Published in at http://dx.doi.org/10.1214/08-AAP561 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Heveling, Matthias, Reitzner, Matthias
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PoisFFT - A Free Parallel Fast Poisson Solver [PDF]
, 2014 A fast Poisson solver software package PoisFFT is presented. It is available as a free software licensed under the GNU GPL license version 3. The package uses the fast Fourier transform to directly solve the Poisson equation on a uniform orthogonal grid.
Fuka, Vladimír
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The lower tail: Poisson approximation revisited [PDF]
, 2014 The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form.
Janson, Svante, Warnke, Lutz
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