ISSN:
1432-2064
Keywords:
60B10
;
60F05
;
60F10
;
60B15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary A second order error bound is obtained for approximating ∫h d $$\tilde Q$$ by ∫h d $$\tilde Q$$ , where $$\tilde Q$$ is a convolution of measures andQ a compound Poisson measure on a measurable abelian group, and the functionh is not necessarily bounded. This error bound is more refined than the usual total variation bound in the sense that it contains the functionh. The method used is inspired by Stein's method and hinges on bounding Radon-Nikodym derivatives related to $${{d\tilde Q} \mathord{\left/ {\vphantom {{d\tilde Q} {dQ}}} \right. \kern-\nulldelimiterspace} {dQ}}$$ . The approximation theorem is then applied to obtain a large deviation result on groups, which in turn is applied to multivariate Poisson approximation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01246337
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