Distance Estimates for Poisson Process Approximations of Dependent Thinnings
نویسندگان
چکیده
منابع مشابه
Distance estimates for Poisson process approximations of dependent thinnings
It is well known, that under certain conditions, gradual thinning of a point process on R+, accompanied by a contraction of space to compensate for the thinning, leads in the weak limit to a Cox process. In this article, we apply discretization and a result based on Stein’s method to give estimates of the Barbour-Brown distance d2 between the distribution of a thinned point process and an appro...
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In [Schuhmacher, Electron. J. Probab. 10 (2005), 165–201] estimates of the Barbour-Brown distance d2 between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization with a result based on Stein’s method. In the present article we concentrate on point processes that have a density with respect to a Poisson process, for which ...
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Although the study of weak convergence of superpositions of point processes to the Poisson process dates back to the work of Grigelionis in 1963, it was only recently that Schuhmacher [Stochastic Process. Appl. 115 (2005) 1819–1837] obtained error bounds for the weak convergence. Schuhmacher considered dependent superposition, truncated the individual point processes to 0–1 point processes and ...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2005
ISSN: 1083-6489
DOI: 10.1214/ejp.v10-237