 Stein's method and point process approximationA. D. Barbour and T. C. Brown Stochastic Processes and their Applications, 1992, vol. 43, issue 1, 9-31 Abstract: The Stein-Chen method for Poisson approximation is adapted into a form suitable for obtaining error estimates for the approximation of the whole distribution of a point process on a suitable topological space by that of a Poisson process. The adaptation involves consideration of an immigration-death process on the topological space, whose equilibrium distribution is that of the approximating Poisson process; the Stein equation has a simple interpretation in terms of the generator of the immigration-death process. The error estimates for process approximation in total variation do not have the 'magic' Stein-Chein multiplying constants, which for univariate approximation tend to zero as the mean gets larger, but examples, including Bernoulli trials and the hard-core model on the torus, show that this is not possible. By choosing weaker metrics on the space of distributions of point processes, it is possible to reintroduce these constants. The proofs actually yield an improved estimate for one of the constants in the univariate case. Keywords: Poisson; approximation; point; process; Stein-Chen; method; coupling; Palm; probability; immigration-death; process; hard-core; model (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:43:y:1992:i:1:p:9-31 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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