1 results
Rates of convergence for random approximations of convex sets
- Part of
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- Journal:
- Advances in Applied Probability / Volume 28 / Issue 2 / June 1996
- Published online by Cambridge University Press:
- 01 July 2016, pp. 384-393
- Print publication:
- June 1996
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- Article
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The Hausdorff distance between a compact convex set K ⊂ ℝd and random sets
is studied. Basic inequalities are derived for the case of 
being a convex subset of K. If applied to special sequences of such random sets, these inequalities yield rates of almost sure convergence. With the help of duality considerations these results are extended to the case of 
being the intersection of a random family of halfspaces containing K.
is studied. Basic inequalities are derived for the case of 
being a convex subset of 
being the intersection of a random family of halfspaces containing 